The octagon shown below has eight congruent sides. The given measures of the octagon are rounded to the nearesttenth of a centimeter.11.6 cm8.2 cm28 cm8.2 cm- 28 cmWhat is the area, to the nearest square centimeter, of the octagon?A.392B. 487C. 650D. 720
Accepted Solution
A:
Answer:Option C [tex]650\ cm^2[/tex]Step-by-step explanation:we know thatThe area of the octagon can be divided in two trapezoids and one rectanglesoThe area of the octagon is equal to the area of the two trapezoids plus the area of rectanglestep 1 Find the area of one trapezoidThe 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 rectangleThe 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]