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 .
[tex] GP= 2-(-3) = 2+3 =5
\\
PS = 4-(-3) = 4+3=7
\\
Area = 5* 7= 35 square \ units [/tex]
And for triangle , area is half of the product of height and base.
For the given triangle,
[tex] Height = 4-2=2 \\
base=4-(-3)=7 \\
Area=(1/2)2*7 = 7 \ square \ units [/tex]
Total area of the polygon is the sum of areas of rectangle and triangle , that is
[tex] Total \ area = 35+7 = 42 \ square \ units [/tex]
