What is the area of the regular octagon below?
A) 114.5 m (sqrt 2)
B) 229.1 m (sqrt 2)
C) 391.1 m (sqrt 2)
D) 458.2 m (sqrt 2)

The answer is 229.1 m²

Step-by-step explanation:

Area of a regular polygon is 1/2 times perimeter times apothem.

use sine to find out the base of the triangle, which is about 3.4 then multiply that by 2 to get the full length of one side of the octagon. once you've found that, 6.888301782, multiply it by 8 to get the perimeter. The perimeter of the octagon is 55.10641426.

next find the apothem (the dotted line), use cosine laws to find it. the apotherm is 8.314915793.

now put it all together, A=1/2ap:

.5 ×8.314915793×55.10641426 = 229.1025971

rounded to the nearest tenth, the area is 229.1 m²

answer: 5000

step-by-step explanation: