Answer:
Option C [tex]650\ cm^2[/tex]
Step-by-step explanation:
we know that
The area of the octagon can be divided in two trapezoids and one rectangle
so
The area of the octagon is equal to the area of the two trapezoids plus the area of rectangle
step 1
Find the area of one trapezoid
The area of one trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]H[/tex]
we have
[tex]b1=28\ cm[/tex]
[tex]b2=11.6\ cm[/tex]
[tex]H=8.2\ cm[/tex]
substitute
[tex]A=\frac{1}{2}[28+11.6]8.2[/tex]
[tex]A=162.36\ cm^2[/tex]
step 2
Find the area of rectangle
The area of rectangle is
[tex]A=bh[/tex]
we have
[tex]b=28\ cm[/tex]
[tex]h=11.6\ cm[/tex]
substitute
[tex]A=(28)(11.6)[/tex]
[tex]A=324.8\ cm^2[/tex]
step 3
Find the area of the octagon
[tex]A=(2)162.36+324.8=649.52\ cm^2[/tex]
Round to the nearest square centimeter
[tex]649.52=650\ cm^2[/tex]
