Question

What is the area of a polygon with vertices at (-5,5), (-1,5), (5,-3) and (-5,-3)?(1 point) Responses 40 sq units 40 sq units 44 sq units 44 sq units 68 sq units 68 sq units 56 sq units

Answer 1

To find the area of a polygon with vertices, you can use the shoelace formula.

Using the coordinates given:
(-5,5), (-1,5), (5,-3), (-5,-3)

The formula for calculating the area of a polygon using the shoelace formula is:

Area = 1/2 |(x1y2 + x2y3 + ... + xn y1) - (x2y1 + x3y2 + ... + x1yn)|

Calculating,

Area = 1/2 |(-5*5 + -1*-3 + 5*-3 + -5*5) - (5*-1 + -3*5 + -3*-5 + 5*-5)|
Area = 1/2 |-25 + 3 - 15 - 25 - 5 + 15 + 15 - 25 |
Area = 1/2 |-57|
Area = 1/2 * 57
Area = 1/2 * 57
Area = 28.5 square units

Therefore, the area of the polygon is 28.5 square units.