A model of the picture shown below is to be made from a 30 cm long wire. Find the dimensions of the sides of the figure so that its area is maximum.

The figure below shows a rectangle with sides a and b.

Express the perimeter of the given rectangle using the variables a and b.
Express the area of the given rectangle using the variables a and b.
Calculate the perimeter of the rectangle if you measure the sides and .
Calculate the area of the rectangle if the sides measure and .

A given quadrilateral with vertices , and Calculate its area.

Calculate the distance of the line from the coordinate origin. Calculate the distance using the area of the triangle formed by the line with the coordinate axes .

The area of a rectangle with perimeter is . What is the length of the diagonal of the rectangle?

The diagram below shows a right-angled triangle ABC. The length of side a is 4.72 cm, and the right-angled triangle projection of side a on the hypotenuse c is 2.50 cm. Using the height theorem, calculate the perimeter of the triangle.

10.

The rectangle ABCD with area is divided into a square and a rectangle as shown in the figure. What is the length of the square if the side of the rectangle is smaller than the side of the square?

11.

The figure below shows a square with side a.

Express the perimeter and area of the square in terms of the variable a.
Calculate the perimeter of the square if the length measures .
Calculate the area of the square if the length measures .

12.

Solve the following tasks:

Given a with the parameters , , as measures . Calculate both possible page lengths . Round the result to two decimal places.
The lengths of the sides of a triangle are three consecutive terms of an arithmetic sequence with difference d = 1. Calculate the lengths of the sides if the largest angle of the triangle measures .
In the triangle measure the sides and . Between the angles and the connection applies. Calculate the area of triangle . Round the result to two decimal places.

13.

Given the coordinates of the vertices of a triangle as:

find the perimeter of the triangle.

14.

The diagram below shows triangle ABC. Given that the angle is 86.33°, and is 33.67°, and side b is 7cm. Calculate the perimeter of the triangle .

15.

How much do the sides of a rectangular plot of land with perimeter and area measure?

16.

The diagram below shows an isosceles triangle ABC. The angle of the triangle in the isosceles triangle is 50°, and side a is 5.52 cm. Calculate the perimeter and area of the triangle.

17.

The plot of land with the area has the shape of a rectangle. You would need fences to enclose it. Calculate the width and length of the land.

18.

The cuboid above is 15 cm long, 6 cm wide and 8 cm high. Calculate the area of the marked cross section of the cuboid.

19.

In what ratio are the length and width of a rectangle of length if its area is ?

20.

Given the coordinates of the vertices of a triangle as:

find the perimeter of the triangle.

21.

The diagram below shows a triangle ABC. The perimeter of the isosceles triangle is 16 cm and the side a is 6 cm long. Calculate the area of the triangle .

22.

In what ratio are the length and width of a rectangle with perimeter and width ?

23.

In a right-angled triangle with hypotenuse , the legs are in ratio . Calculate the lengths of the legs of this right-angled triangle.

24.

Calculate the area of the shaded region in the diagram below to one decimal place.

25.

The points , and are given. Calculate the perimeter and area of .

26.

One side of a parallelogram measures 8cm, and an angle is 70°. The area of the parallelogram is 30.08. Calculate the perimeter of the parallelogram.

27.

The points , and are given. Calculate the perimeter and area of .

28.

A rectangle with sides of 10 cm and 4 cm is folded to form a cylinder.

Draw the sketch and calculate the area of the resulting cylinder to the nearest .
Calculate the length of the longest rigid rod that could still be hidden in this cylinder.
How much angle does this rod enclose with the base surface of the cylinder? As indicated in the sketch.

29.

Calculate the area of the given triangle below in two different ways.

30.

The sides of a parallelogram measures 8 cm by 6 cm and the longer diagonal is 8 cm. Calculate the interior angles and the area of the parallelogram.

31.

The perimeter of a regular heptagon is . Calculate the length of a side of the polygon.

32.

Solve the following problems in geometry:

In the circle with radius we draw a rectangle whose sides are in the ratio . Calculate the perimeter of the rectangle. What percentage of the area of the circle is the area of the rectangle?
In a rhombus, the difference of diagonals is , and its area measures . Calculate the lengths of the diagonals and its side. Leave the result in surd form.
The sides of the triangle represent the first three terms of an arithmetic sequence with a difference of 4. The plane of the triangle is . Calculate the lengths of the sides.

33.

A quadrilateral has vertices , , and .

Draw the quadrilateral in the coordinate system.
Calculate the area of a quadrilateral.
What percentage of the area of a quadrilateral ABCD represents the area of a triangle ABD?

34.

Calculate the perimeter of a given hexagon with side: .

35.

Calculate the perimeter and area of a regular decagon shown in the figure below.

36.

If a column support has a hight of about , volume of about and it also has the shape of an oblique equilateral cylinder. Calculate the angle of inclination .

37.

Calculate the perimeter and area of the regular pentagon shown below:

38.

If we increase one side of a square by and decrease the other side of it by , we get a rectangle that has the same area as the square. Calculate the perimeter and sides of both shapes.

39.

Calculate the perimeter and area of the cube grid. The cube has a side long .

40.

A side of the parallelogram measures 6 cm with height 4.11 cm. If it has an angle 36 °. Calculate the area and diagonals of the parallelogram.

41.

Calculate the unknown quantities for the regular polygons and complete the table.

Number of sides	Length	Perimeter

42.

The perimeter of a rectangle with area is . What is the measurement of the rectangle?

43.

The area of a negatively oriented triangle ABC with vertices and is equal to . Calculate the value of x, the x- coordinate of the vertex B.

44.

In an octagon with a perimeter of , three sides measures , two sides , one side by , and another by . Find the missing side of the polygon?

45.

We would like to enclose a rectangular beam with a surface of . What are the dimensions of the beam if its perimeter is equal to .

46.

The coordinates of triangle ABC are: and . Calculate the:

perimeter of the triangle,
area of the triangle,
size of angle , to the nearest hundredth degree.

47.

Points , and are the vertices of a triangle in a right-angled coordinate system. Determine the orientation of the triangle and calculate the area if the coordinates of the points are:

, and .

48.

A midline drawn from the midpoint of the two non parallel side of a trapezium measures 6.5 cm with height 3 cm and an interior angle 52 °. The perimeter of the trapezium is 19.83 cm. Calculate the area of the trapezium, one of the non parallel side, and the remaining interior angles.

49.

Transform the parallelogram in the figure into a rectangle and calculate its area.

50.

The height of a trapezium measures 5 cm and two of its interior angles are 46 ° and 124 °. The area of the trapezium is 40. Calculate the remaining interior angles and the perimeter of the trapezium.

51.

Calculate the area of all diagonal sections of a cuboid whose length is 5 times and height 3 times of width measuring 7 cm.

52.

A side of a parallelogram measures 8cm and the height perpendicular to the given side is 2.58cm. If an angle of the parallelogram is 31°, calculate its perimeter and area.

53.

The longer diagonal of a trapezium is 9.56 cm, its two parallel sides are 10 cm and 8 cm while one of the non-parallel sides is 3 cm. Calculate the area of the trapezium.

54.

In an isosceles triangle in which side b is longer than side a, side , height and median from vertex C is . Calculate the side c and the area of the triangle. Make a sketch.

55.

Calculate the perimeter of the given triangle. study the data from the graph or calculate the perimeter.

56.

The height of a parallelogram measures 5cm and one of its angles is 45.58°. The area of the parallelogram is 48. Calculate the length of the longer diagonal and the perimeter of the parallelogram.

57.

Points , and are the vertices of a triangle in a right-angled coordinate system. Determine the orientation of the triangle and calculate the area if the coordinates of the points are:

, and .

58.

A side of a parallelogram measures 8 cm, and the shorter diagonal is 12.18 cm. If an angle of the parallelogram is 42 °. Calculate the perimeter and area of the parallelogram.

59.

In a coordinate system, we have points and . Calculate the perimeter and area of the triangle .

60.

A side of a parallelogram measures 6cm, and its longer diagonal is 9cm. If an angle of the parallelogram is 92.73°. Calculate the perimeter and area of the parallelogram.

61.

Points , and are the vertices of a triangle in a right-angled coordinate system. Determine the orientation of the triangle and calculate the area if the coordinates of the points are:

, and .

62.

The length of the longer diagonal of a kite is 10 cm, Two of its interior angles are 97.90 ° and 59.37 °. If the area of the kite is 39.62 , calculate its remaining angle and perimeter.

63.

Draw a coordinate system and indicate points and on it. Calculate the perimeter of triangle .

64.

A side of a kite measures 7.58 cm and its shorter diagonal is 7 cm. One of its interior angle measures 61.93 °. Calculate the perimeter and area of the kite.

65.

Calculate the perimeter of the given triangle.

66.

A side of a kite measures 5.03 cm and its shorter diagonal is 6 cm. If one of its interior angle measures 51 °, calculate the perimeter and area of the kite.

67.

A bathroom measuring 3.6 m long, 3 m wide and 2.4 m high is to be covered with ceramic tiles. If each tile measures 20 cm x 30 cm and the floor is to be completely covered with two adjacent walls, calculate the:

surface area to be covered with ceramic tiles.
number of tiles needed.
If a square meter of tiles costs 15 Naira. How much would be saved if only the floor and the small wall is to be covered?

68.

A side of a parallelogram measures 5cm, and its longer diagonal is 11.58cm. If an angle of the parallelogram is 31°. Calculate the perimeter and area of the parallelogram.

69.

The two sides of a kite are given as 6 and 3 cm and 28 ° is one of its interior angle. Calculate the area of the kite.

70.

Calculate the perimeter and area of triangle ABC in the figure below:

71.

A side of a parallelogram measures 7cm, and its shorter diagonal is 5cm. If an angle of the parallelogram is 135.58°. Calculate the perimeter and area of the parallelogram.

72.

A side of a kite measures 6 cm and its longer diagonal is 11 cm. If one of its interior angle is given as 59.05 °, calculate the perimeter and area of the kite.

73.

A kite has a side length of 5 cm and longer diagonal of 8 cm. If one of its interior angle measures 48.29 °, calculate its perimeter and area.

74.

The area of a kite is . What will be the length of diagonal e, if the length of diagonal f is twice that of diagonal e?

75.

The side of a square measures 5 cm. Calculate the diagonal, perimeter and area of the square.

76.

Calculate the perimeter and area of the kite with the data:

77.

The vertices of a parallelogram ABCD are given as , , .

Graphically find the coordinates of the fourth point D.
Calculate the area of the parallelogram.
Calculate both heights of the parallelogram.
Find the intersection of the diagonals of the parallelogram.

78.

The shorter sides of a kite measures 3.25 cm while its shorter diagonal is 5 cm. If the interior angle between the longer sides is 99.56 °, calculate the perimeter of the kite.

79.

The lengths of the diagonals of a kite are e and f. Compare the area of this kite with the area of a kite whose diagonals are three times longer.

80.

Points , and are given in a plane.

Prove that is right angled. Hence, calculate the area of its circumscribed circle.
Calculate the coordinates of point A', which is the perpendicular projection of point A onto the .
Point M lies on . Write the coordinates of the point M so that the area of the is equal to 11.

81.

The base of a rhombus measures 4 cm and the area is 9.85 . Calculate its interior angles and the perimeter of the rhombus.

82.

Insert points , and into the coordinate system and join them. Calculate the area of the given triangle.

83.

The base of a rhombus measures 4 cm, and one of its interior angle is 139 °. Calculate its perimeter and area.

84.

The base of a rhombus measures 5 cm, and one of its interior angle is 73.74 °. Calculate its longer diagonal and the perimeter of the rhombus.

85.

Calculate the perimeter and area of the kite below, given: and .

86.

The diagram below shows a triangle ABC:

Given that side a in the triangle is 9.40 cm, side c is 10 cm, and the angle is 55.19°. Calculate the area of the triangle.

87.

The base of a rhombus measures 6 cm and its longer diagonal is 10 cm. Calculate all the interior angles and area of the rhombus.

88.

Calculate the perimeter of the triangle with vertices , and . Is it an equilateral or isosceles triangle?

89.

The base of a rhombus measures 4 cm and the length of the shorter diagonal is 1 cm. Calculate all interior angles and the area of the rhombus.

90.

The perimeter of the kite is . Side a is longer than side c. Calculate the length of both sides.

91.

The length of the longer diagonal of a rhombus measures 13 cm and one of its interior angles is 71.32 °. Calculate the perimeter of the rhombus.

92.

Calculate the area of the kite in the figure below.

93.

The area of an equilateral triangle is 21.22 . Calculate the:

length of the sides,
size of the angles, and

perimeter of the triangle.

94.

The area of a rhombus measures 23 and one of its interior angles is 23.04 °. Calculate the perimeter of the rhombus.

95.

The perimeter of a rhombus measures 29.60 cm and its area is 37 . Calculate all the interior angles of the rhombus.

96.

A kite with diagonal lengths and and a kite with diagonal length have the same area. Find the length of the diagonal of the second kite.

97.

The perimeter of a rhombus measures 20 cm and its shorter diagonal is 3.75 cm. Calculate the area of the rhombus.

98.

Calculate the angles , and in the kite shown below.

99.

The length of a rectangle measures 7 cm and its area is 28 . Calculate the diagonal and perimeter of the rectangle.

100.

The angle at vertex B of a kite is . The angle at vertex D, between the axis of symmetry and the side c, is .

Draw a sketch,
calculate the values of the remaining interior angles of the kite.

101.

The length of a rectangle is 4 cm and its diagonal measures 7 cm. Calculate the perimeter and area of the rectangle.

102.

Calculate the angle in the kite.

103.

Points , and are given in the coordinate system. Calculate the area of the triangle bounded by the median, , of the and the coordinates of the origin.

104.

The perimeter of a rectangle is given as 26.72 cm and the area is 39.23 . Calculate the sides of the rectangle.

105.

The diagram below shows an isosceles triangle ABC. The area of an isosceles triangle is 12 and the base c is 6 long. Calculate the altitude to the side c and the perimeter of the triangle.

106.

The perimeter of a rectangle measures 26 cm and the diagonal is 9.43 cm. Calculate the area of the rectangle.

107.

A trapezoid with a perimeter of 20 cm is made from three equilateral triangles. What is:

the area of each of the triangles,
area of the trapezoid?

108.

The length and breadth of a rectangle measure 10 and 6 cm respectively. Calculate the diagonal, perimeter, and area of the rectangle.

109.

A hexagon of area 15.59 is produced from six equilateral triangles. Calculate the:

perimeter of each triangle.
perimeter of the newly formed hexagon.

110.

The area of a trapezium is 23.52 and the midline is 7.84 cm. One of its interior angle is 142 °. Calculate the perimeter of the trapezium.

111.

The diagonal of a rectangle measures 10.30 cm and the area is 45 . Calculate the perimeter of the rectangle.

112.

The perimeter of the kite is , and the length of one of its sides is . Calculate the length of the unknown side.

113.

The area of a square measures 112.50 . Calculate the diagonal and perimeter of the square.

114.

Calculate the perimeter, of a kite with sides and .

115.

The diagonal of a square measures 15 cm. Calculate the perimeter and area of the square.

116.

Calculate the perimeter of the figure below.

117.

The figure below is a triangle

Calculate the perimeter and area of the triangle .
Write the equation of the line through the points and .
The equation of the line through the points and is:

Calculate the size of the angle of the triangle at the vertex.

118.

The perimeter of a square is 16 cm. Calculate the area of the square.

119.

The height of a trapezium measures 3 cm and the midline is 6.33 cm. If its perimeter is 21.63 cm, calculate the area of the trapezium and all its interior angles.

120.

The area of the kite is , and the longer diagonal measures . Calculate the length of the shorter diagonal .

121.

The diagram below shows a right-angled triangle ABC. The hypotenuse c of the triangle ABC is 6.93 cm. The ratio of the lengths of the perpendicular projections of sides a and b to the hypotenuse is 3.00. Calculate the perimeter and area of the triangle.

122.

The area of a trapezium measures 19.41 and the height is 5 cm. One of its interior angles is 100 °. Calculate the perimeter of the trapezium.

123.

A side of trapezium measures 4.87 cm and the length of the diagonal measures 7 cm. If 85.39 ° is one of its interior angles, calculate the area of the trapezium.

124.

The area of a rectangular trapezium measures 39.42 and the midline is 7.88 cm. If one of its angle is 53 °. Calculate the perimeter of the trapezium.

125.

The area of a rectangular trapezium measures 14.36 and the height is 3 cm. If one of its interior angle is 140 °. Calculate the perimeter of the trapezium.

126.

Two sides of a rectangular trapezium measure 7.67 cm and 3.32 cm, and its diagonal is 6 cm. Calculate the area of the trapezium.

127.

The two parallel sides of a rectangular trapezium measure 8.47 cm and 4 cm, and the diagonal is 6 cm. Calculate the area of the trapezium.

128.

Two sides of a rectangular trapezium measure 7.05 cm and 3 cm while the height is 6 cm. Calculate the area and perimeter of the trapezium.

129.

The diagonals of a rectangular trapezium measure 7 cm and 10 cm. One of its side is 3 cm. The perimeter of the trapezium is 24.05 cm. Calculate all interior angles of the trapezium.

130.

The sides of a parallelogram are 6 cm and 4 cm. One of its interior angle is . Calculate the area and the length of the longer diagonal.

131.

The diagonals of a rectangle intersect at the center of the rectangle. If the length of the rectangle measures 10 cm and the angle formed at the meeting point of the diagonals is . Calculate the perimeter of the rectangle. Round the result to one decimal place.

132.

The perimeter of a parallelogram measures 26 cm and one of its interior angle is 57 °. If the length of its height and one of its side are equal, calculate the area of the parallelogram.

133.

Equations of straight lines are given below, draw the lines on a graph:

Calculate the perimeter and area of the quadrilateral bounded by these lines.

134.

A square is inscribed in another bigger square. Find the ratios of their areas and perimeters.

135.

In a trapezium , the parallel sides measure , and the diagonal is . If the diagonals are equal, calculate the:

height and the unknown side.
angle between the diagonals.
surface area and volume.

136.

A rhombus has a side 6 cm and an angle formed between a side and the height is . Calculate the interior angles and the height of the rhombus.

137.

The area of a rectangle inscribed in a square measures . Calculate the perimeter of the square if the ratio of the length to the breadth of the rectangle is :.

138.

The length of a rectangle measures 20cm and the diagonal is 25cm. Calculate the perimeter and area of the rectangle.

139.

A diagonal of a square divides the square into two halves, if a rectangle is inscribed in one of the halves and the dimensional ratio of the square to the rectangle is 3: 2, calculate the area of the rectangle when the perimeter of the square measures 28 cm.

140.

The parallel lengths of a trapezium measure 7 cm and 4 cm. If its height also measure 4 cm and two of its interior angles are right angle, calculate the:

perimeter and area of the trapezium.
remaining interior angles of the trapezium.
length of its shorter diagonal.

141.

The diagonals of a rhombus are 16 cm and 12 cm. Calculate its perimeter.

142.

Two identical rectangular boards with a width of 12 cm are inclined over one another at an angle of . The region of their intersection formed a rhombus. Calculate the area of the rhombus.

143.

A rectangular garden has length of 10m and a width of 6m. If there is an increase in the length of the garden by 20% and decrease in the width by 15%. Calculate the difference in the area of the garden.

144.

Lines p, q and r are drawn on a graph. These three lines and the x-axis enclosed to form a parallelogram. Write the equations of the lines and calculate the area and perimeter of the parallelogram.

145.

The area of the figure below measures 10.28 . Calculate its perimeter.

146.

If the total area of an equilateral triangle and a rhombus is increased by 20%, area of a square is the obtained result. What is the size of the interior angles in the rhombus if all three shapes have equal base a?

147.

An equilateral triangle, a square and an hexagon are circumscribed by circles. If the circles are equal in circumferences. What is the ratio of the sides of the figures?

148.

An equilateral triangle ABC with a perimeter of 14 cm is divided by a midline into a smaller triangle and a trapezium. The midline of the trapezium formed is equal to the diameter of a circle. Calculate the area of the circle.

149.

The angle in a right-angle triangle is 41°, and the length of the hypotenuse c is 10.67cm. Calculate the perimeter and area of the triangle.

150.

The angle in a right-angled triangle is 50°, and the length of side a is 5cm. Calculate the perimeter and area of the triangle.

151.

The perimeter of a right-angled triangle is 22.36cm and the angle is 49°. Calculate the length of the hypotenuse c and the area of the triangle.

152.

The outer frame of the picture is a rectangle of dimensions . The frame of the image is equally wide at all four sides. The inner frame is an image with as area. Calculate the width of the frame.

153.

In a right-angled triangle, side a is 4.77 cm, and the quotient of the lengths of the right projections of side a and b on the hypotenuse is 1.52. Calculate the perimeter of the triangle.

154.

In a right-angled triangle, the length of side a is 5.20 cm and the projection of the side c on the hypotenuse c is 6.93 cm. Calculate the area of the triangle.

155.

In a right-angled triangle, the length of side b is 8.37 cm, and the projection of the side b on the hypotenuse c is 7.82 cm. Using Euclid's theorem, calculate the area of the triangle.

156.

The area of a right-angled triangle is 17.80 . The length of side b is 7.55 cm, and the perpendicular projection of side a on the hypotenuse c is 2.50 cm. Using the height theorem and both Euclidean theorems, calculate the length of each side of c and the perimeter of the triangle.

157.

From two equilateral triangles, we construct a rhombus whose longer diagonal is 8.66 cm. Calculate the perimeter and area of the rhombus.

158.

Two lines are given:

Draw the two lines in the same coordinate system and calculate their intersection.
Calculate the area of the triangle defined by the lines and the abscissa axis.
Calculate the maximum interior angle of the triangle to the nearest minute.

159.

From nine equilateral triangles with height 4.33 cm we form a larger equilateral triangle. Calculate the perimeter and area of the larger equilateral triangle.

160.

Draw the lines with the equations in the coordinate system:

and calculate the area of the triangle they enclose.

161.

In an isosceles triangle, the base is 16 cm and the length of the sides is 10 cm. Calculate the perimeter, the height from the base, the area of the triangle and the angle at the base to the nearest tenth of a degree.

162.

In a given isosceles triangle ABC the height , angle . Calculate the length of the base, the side and area of the triangle. Round the result to 3 decimal places.

163.

In a given isosceles triangle ABC, the lengths of side and . Calculate the area of the triangle and the angle of triangle ABC. Round the value of the angle to the hundredth of a degree.

164.

In a right-angled triangle ABC with right angles at the C angle, the length of side cm, and the angle at the vertex A is . Calculate the area of this triangle.

165.

Equilateral triangle ABD with side 3 cm and height 5.2 cm mirrored over line p. What is the area of the figure thus formed which consists of the basic triangle and its mirrored image?

166.

The square in the figure is halved with a vertical bisector and the right half is moved up by half the length of the side of the original square. Which polygon do we get?

167.

A square of area is inscribed in a circle. Calculate the area of the circle and express it in square decimetres. Round the final result to two decimal places.

168.

Calculate the perimeter of an isosceles trapezoid with base length 4a. The length of the parallel side to the base is equal to half the base. The length of each of the two unparallel sides is a.

169.

Calculate the unknown x and the perimeter of the parallelogram in the figure below. All units are in centimetres.

170.

Calculate the unknown value x and the perimeter of the parallelogram in the figure. All units are in centimetres.

171.

Calculate the perimeter and area of an equilateral triangle if the length of the side is .

172.

The sum of the squares of the sides in a right triangle is equal to 225 and is 204 longer than the sum of the sides. Calculate the perimeter of this triangle.

173.

Calculate the perimeter and area of a right triangle in which hypotenuse a is long, one side is and the other is .

174.

Find x so that the perimeter of the triangle is . Hence find the sides of the triangle.

175.

The parallelogram ABCD is given:

Calculate its perimeter.
Finds how many times side b is longer (or shorter) than side a.

176.

One side of a right triangle is shorter than the hypotenuse, and the other side is . Calculate the perimeter and area of this triangle.

177.

The figure is given:

Calculate:

area of a right triangle,
the number of squares above the hypotenuse c, if the square is divided into smaller squares in the same way as the two squares above the legs are divided,
sides of a right triangle and
the perimeter of the triangle.

Find out the necessary information with the help of a picture. Take that the side of the square is long.

178.

The height of an isosceles triangle is shorter than the sides and longer than the base. Calculate the lengths of all three sides, the height h and the area if the perimeter is .

179.

The perimeter of a right triangle is . Calculate its area if one side is shorter than the hypotenuse by and longer than the other side by . Use a calculator to check that this triangle is indeed right-angled.