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is given with the parallel sides 
and 
, the legs 
and 
measure 
each. The legs are extended to intersect at point 
, to form an isosceles triangle, 
. Calculate the length of side 
. (Hint: A sketch is required).
, and its perimeter measures 
. How much do the sides of the quadrilateral measure?
, base AB is 
. Point D is the midpoint of the base AB. The point E is the foot (rectangular projection of the point B on the side AC) of the height on the side AC. Draw a sketch.
we have 
and 
. Side 
is 
shorter than side 
.
and 
of a rhombus with its side 
are in ratio 
. What are the lengths of the diagonals?
, the height passes through the vertex 
and intersects:
at point 
and
at point 
.
divides line 
in the ratio 
, calculate the perimeter of triangle 
.
, for which:
is the mid-segment of triangle ABC
, we draw a parallelogram 
in the ratio 
. What is the perimeter of 
measures 
?
. The perpendicular bisector of the hypotenuse, 
, cuts the base 
at point D in the ratio:
. What is the length of the other sides of the triangle?
in the figure below, calculate the lengths of the unknown 
and 
:
with point 
being an intersection of lines projected from point 
and 
making 
. The base of the trapezium is 
long. The perimeter of the trapezium ABCD is 
and the perimeter of the triangle ABE is 
. Calculate the area of the trapezium 
if their areas are in the ratio 
.
with side 
, the perpendicular projection of the point of intersection of the diagonals divides the side AB of the rhombus into two parts. If each part measures 
and 
find the:
below to get a rectangle 
.
with sides 
, 
and 
is given. On side 
lies the point 
so that 
. Calculate length of side 
.
has bases 
and 
and diagonal length 
. The diagonal 
divides the diagonal 
into two parts. Calculate the length of each part?
has points 
and 
located inside it. The point 
and point 
from the centre of the circle, 
. The distance between points 
. Let 
and 
be points outside the circle which lie on the extensions of lines SA and SB, respectively, such that 
and 
. Use the radius 
and 
in the ratio 
is inscribed in an isosceles triangle as shown in the diagram.
long, the slant height 
and side 
of the rectangle lies on the base of the triangle, calculate the area of the rectangle.
long cylindrical rod, a one meter long string is wrapped four times. The beginning of the string is at the top edge of the rod. Just below it, on the lower edge of the rod, is the end of the string as shown in the diagram.
from the origin.
. 
is a right angled triangle inscribed in the circle. The right angle of 
. The length of the hypotenuse of 
, the length of the other sides are in the ratio 
. Draw a tangent line which makes a point of contact with the circle at the vertex 
of the right angle triangle. The point 
is the intersection of the tangent and a line that bisects the 
. Calculate the distance 
of the point 
is given with the bases measuring 
and 
and the shorter leg as 
. The legs intersect at the point 
, which is 
away from the vertex 
. This is shown in the figure below:
.
