Answer :
Answer:
Part 1) The area of the polygon is [tex]42\ units^{2}[/tex]
Part 2) The area of the polygon is [tex]43.5\ units^{2}[/tex]
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
[tex]A=bh=5*7=35\ units^{2}[/tex]
Find the area of triangle
[tex]A=(1/2)bh=(1/2)*7*2=7\ units^{2}[/tex]
The area of the figure is equal to
[tex]35\ units^{2}+7\ units^{2}=42\ units^{2}[/tex]
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
[tex]A=(1/2)bh=(1/2)*3*2=3\ units^{2}[/tex]
Find the area of triangle 2
[tex]A=(1/2)bh=(1/2)*5*1=2.5\ units^{2}[/tex]
Find the area of trapezoid
[tex]A=(1/2)(b1+b2)h=(1/2)*(11+8)*4=38\ units^{2}[/tex]
The area of the figure is equal to
[tex]3\ units^{2}+2.5\ units^{2}+38\ units^{2}=43.5\ units^{2}[/tex]
see the attached figure N 2 to better understand the problem