The Ruffs are planning to buy an above-ground swimming pool shaped as a regular octagon. The radius of the octagon is 9 feet. To the nearest tenth, find the area of the surface of the water in the pool.
Possible answers:
A) 458.2 ft2
B) 553.1 ft2
C) 94.8 ft2
D) 229.1 ft2
octagon can be split into 8 equal isosceles triangles
Area of octagon will be 8X area of each triangle
360/8 = 45
top angle opposite of base is 45 degrees
180(8-2) = 1080, this is sum of interior angles
1080/8 = 135
135/2 = 67.5
bottom 2 angles opposite of radii are 67.5 degrees
to find area of triangle we need base length(x) and height(h)
use trig ratios
h = 9sin(67.5)
x = 18cos(67.5)
Area = 8*(1/2)*(9sin(67.5))*(18cos(67.5))
Area = 648*sin(67.5)*cos(67.5)
Area = 229.1
