1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm. 2)What is the area of each triangle?

3)What is the area of the octagon?

4) Use your work from above to derive a generic formula for any octagon with side length that is n units.

(a)

(b)

(c)

Step-by-step explanation:

Given

--- base

--- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

--- i.e. we consider half of the triangle

Solve for h

The area of each triangle is:

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

Solving (c): Area of octagon of side length n

In (a), we have:

Replace b with n

Multiply by 8 (the sides) to get the area of the octagon

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step-by-step explanation:

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