Question

(05.05)Polygon ABCD has the following vertices:

A(−5, 4), B(1, 4), C(6, −4), and D(−5, −4)

Calculate the area of the polygon.

Answer 1

`A=68units^2`

Explanation:

First of all, let's plot all the points, so we get the first figure below. Since a Polygon is a shape with straight sides and closed, then if we draw lines in order for the shape to be closed, we get the shape as shown in the second figure. This polygon is a trapezoid because at least one pair of opposite sides are parallel. To get the area, we know the formula:

`For \ any \ trapezoid: \\ \\ A=((b_(1)+b_(2))h)/(2) \\ \\ b_(1) \ and \ b_(2) \ are \ the \ two \ parallel \ bases \\ \\ h \ is \ the \ height`

From the second figure, we know:

`b_(1)=6 \\ \\ b_(2)=11 \\ \\ h=8 \\ \\ Then: \\ \\ A=((6+11)* 8)/(2) \\ \\ \boxed{A=68units^2}`