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