Question

What is the area of this polygon? Enter your answer in the box. units²

Answer 1

To find the area of the given polygon, first we will join P and S .

So we have two figures here, a rectangle GPST, and a triangle , PES .

Area of rectangle is length times width .

For the given rectangle, area is GP times PS .

$GP= 2-(-3) = 2+3 =5 \\ PS = 4-(-3) = 4+3=7 \\ Area = 5* 7= 35 square \ units$

And for triangle , area is half of the product of height and base.

For the given triangle,

$Height = 4-2=2 \\ base=4-(-3)=7 \\ Area=(1/2)2*7 = 7 \ square \ units$

Total area of the polygon is the sum of areas of rectangle and triangle , that is

$Total \ area = 35+7 = 42 \ square \ units$

Answer 2

A = (5 x 7) + 1/2(7)(2)
A = 35 + 7
A = 42

answer
42 units²