Question

1. What is the area of this polygon?

2. What is the area of this polygon?



43.5 units²

45.5 units²

46.5 units²

49.5 units²

Answer 1

Part 1) The area of the polygon is
`42\ units^(2)`

Part 2) The area of the polygon is
`43.5\ units^(2)`

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