what is the area of a regular octagon with a side of 8 in. Round to the nearest tenth, show work please
Length of each side of a regular octagon = 8 inches
We already know the formula for finding the area of a regular octagon as
Area = 2 (1 + square root 2) (Side)^2
= 2 (1 + 1.414) (8)^2
= 2 (2.414) * 64
= 308.99 inches ^2
= 309 inches ^2
So the area of the regular octagon having sides of 8 inches is 309 square inches. This is the easiest method for solving these kind of problems.
Answer:
The area of the regular octagon having sides of 8 inches is 309 square inches.
Step-by-step explanation:
It is given that Length of each side of a regular octagon is 8 inches.
Now, the formula for finding the area of a regular octagon is:
\({\text}{Area}=2(1+\sqrt{2}){\times}(Side)^2\)
Substituting the given values, we get
\(A=2(1+1.414){\times}(8)^2\)
\(A=2(2.414){\times}64\)
\(A=308.99{in^2\)
\(A\)≈\(309 in^2\)
Thus, the area of the regular octagon having sides of 8 inches is 309 square inches.