Question

1. What is the area of this polygon?

Answer 1

Answer:

Part 1) The area of the polygon is $42\ units^{2}$

Part 2) The area of the polygon is $43.5\ units^{2}$

Step-by-step explanation:

Part 1) we know that

The area of the figure is equal to the area of rectangle GPST plus the area of triangle PES

Observing the graph

Find the area of rectangle

$A=bh=5*7=35\ units^{2}$

Find the area of triangle

$A=(1/2)bh=(1/2)*7*2=7\ units^{2}$

The area of the figure is equal to

$35\ units^{2}+7\ units^{2}=42\ units^{2}$

see the attached figure N 1 to better understand the problem

Part 2) we know that

The area of the figure is equal to the area of two triangles  plus the area of a trapezoid

Observing the graph

Find the area of triangle 1

$A=(1/2)bh=(1/2)*3*2=3\ units^{2}$

Find the area of triangle 2

$A=(1/2)bh=(1/2)*5*1=2.5\ units^{2}$

Find the area of trapezoid

$A=(1/2)(b1+b2)h=(1/2)*(11+8)*4=38\ units^{2}$

The area of the figure is equal to

$3\ units^{2}+2.5\ units^{2}+38\ units^{2}=43.5\ units^{2}$

see the attached figure N 2 to better understand the problem