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Perimeter and Area of a Plane Shape
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Perimeter and area of a triangle in the coordinate plane for KS4

The triangle is explained in more detail in the material Triangle. In this material, we will look at the role of the determinant in calculating the area of a triangle.

Let us define a triangle *ABC* in the plane of three (nonlinear) points *A*, *B* and *C*.

The perimeter of the triangle *ABC* is calculated by summing the distances between the points *A* and *B* between *B* and *C* and between *C* and *A*:

where *d* is the length of the line between two points, e.g.

determines the length between the points *A* and *B*.

The area of a triangle in a plane is calculated using the **determinant**.

The determinant is generally written as

where *a*, *b*, *c* and *d* are any real numbers.

The determinant is important because it can be used to calculate the area of a triangle. Given three vertices of a triangle:

the area of the triangle is calculated according to the form:

where:

The area of the triangle is calculated using the form:

Triangle *ABC* is **positively oriented** if the vertices *A*, *B* and *C* follow counterclockwise and **negatively oriented** if the vertices follow clockwise.

If:

*D> 0*, the triangle is positively oriented;*D <0*, the triangle is negatively oriented;*D = 0*, points*A*,*B*and*C*lie on the same line.

material editor: Onyinyechi Cynthia. Natha-Amadi