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Area of a Regular Octagon

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Area of a Regular Octagon

By Carson Dial

Now, for the basics

This is a regular octagon, an 8-sided figure whose sides are congruent.

The small lines on the edges indicate the

congruency of said edges.

Now, we can begin…

First, there is no way to find the area of an octagon by itself, you must divide the octagon into equilateral triangles, eight of them.

Continuing on now…

We need to find the area of a single equilateral triangle.

So we’ll say the length of

this triangle’s base is 5

units.

5

Next up…

We’ll need the height of this triangle,

so for convenience's sake, we’ll call it 6.5 units.

6.5

5

Now, to work this through…

The equation looks something like this

B*h/2 or,

Base times height divided by 2

So, we’ll substitute our numbers in…

5*6.5/2

6.5

5

6.5

* 5

= 32.5 / 2= 16.25

So, the area of this triangle is 16.25 units.

Up next, the full area…

Now, we will multiply the area of the triangle by eight to find the area of the octagon.

- 16.25
- 8
- --------
- 132