Question

2. Find the area of the regular polygon.

*HINT* - You must solve for the side of the octagon before you can find the area of the figure.

a. What is the Perimeter of the figure?


b. What is the area of the figure?

Answer 1

a. 80 units

b. 482.843 units²

Explanation:

First things first, we need to solve for the side of the octagon. We can do so by using Pythagorean Theorem: a² + b² = c² where c is the hypotenuse and a and b are the other two sides.

12² + b² = 13²

144 + b² = 169

b² = 25

b = 5

Now that we know half of the side of the octagon is 5, we know that one side of the octagon is 10.

a. To find perimeter we just add every side together (or since every side is the same size, we multiply by 8)

10 × 8 = 80

b. The formula for finding the area of an octagon is 2(1 + radical 2)a² where a is the length of a side. By plugging in to a calculator we get:

2(1 + radical 2)(10)² = 482.843