(HELP?)
A gardener must replace the shingles on the roof of a gazebo. The roof is a regular octagon. Each side is 8 feet long, and the apothem is 9.66 feet. Find the area of the roof that must be shingled.

A.39 ft
B.78 ft
C.233 ft
D.309 ft

Question

(HELP?)
A gardener must replace the shingles on the roof of a gazebo. The roof is a regular octagon. Each side is 8 feet long, and the apothem is 9.66 feet. Find the area of the roof that must be shingled.

A.39 ft
B.78 ft
C.233 ft
D.309 ft

anonymous · Answer

i got 39^2 for this one but it was wrong..

anonymous · Answer

|dw:1371755459231:dw| We get 8 congruent isosceles triangles, each with height of 9.66 and a base of 8. Finding the area of this triangle and multiplying it by 8 will give us the area of the octagon. $$\bf Area \ of \ triangle= \frac{ 8 \times 9.66 }{ 2 }=38.64 \ ft.$$Multiply this area by 8 to get the area of the octagon:$$\bf Area \ of \ octagon = 38.64 \times 8 = 309.12 \ ft.$$
@ashleyvee