Question

(05.05)Polygon ABCD has the following vertices:

A(−3, 3), B(5, 5), C(5, −4), and D(−3, −4)

Calculate the area of the polygon.

A. 52 units squared
B.56 units squared
C. 64 units squared
D.72 units squared

Answer 1

C. 64 units squared

Answer 2

C. 64 unit squared

Explanation:

We are given a polygon ABCD having co-ordinates A(−3, 3), B(5, 5), C(5, −4), and D(−3, −4).

As, we know that,

Area of a polygon =
`|((x_(1)y_(2)-y_(1)x_(2))+(x_(2)y_(3)-y_(2)x_(3))+(x_(3)y_(4)-y_(3)x_(4))+(x_(4)y_(1)-y_(4)x_(1)))/(2)|`

So, after substituting the values of the co-ordinates, we have,

Area of the polygon =
`|((-3* 5-3* 5)+(5* -4-5* 5)+(5* (-4)-(-4)* (-3))+(-3* 3-(-4)* (-3)))/(2)|`

i.e. Area of the polygon =
`|((-15-15)+(-20-25)+(-20-12)+(-9-12))/(2)|`

i.e. Area of the polygon =
`|(-30-45-32-21)/(2)|`

i.e. Area of the polygon =
`|(-128)/(2)|`

i.e. Area of the polygon = |-64| unit squared.

i.e. Area of the polygon = 64 unit squared.

Hence, area of the given polygon is 64 unit squared.