Question

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

Answer 1

To find the area of the polygon with the given vertices, you can use the shoelace formula. The formula calculates the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) as follows:

Area = 0.5 * |(x1*y2 + x2*y3 + ... + xn*y1) - (y1*x2 + y2*x3 + ... + yn*x1)|

In this case, the vertices are:
A = (-5,5)
B = (-1,5)
C = (5,-3)
D = (-5,-3)

Substitute the coordinates into the formula:

Area = 0.5 * |((-5*5) + (-1*-3) + (5*-3) + (-5*-3)) - (5*-1 + 5*5 + -3*-5 + -3*-5)|

Area = 0.5 * |(-25 + 3 - 15 + 15) - (-5 + 25 + 15 + 15)|

Area = 0.5 * |-22 - 50|

Area = 0.5 * 28

Area = 14 sq units

Therefore, the area of the polygon is 14 sq units.