Answer:
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