Area Of A Regular Octagon

You can calculate the expanse of a regular octagon with the standard regular polygon method, but there's a nifty alternative method based on the fact that a regular octagon is a square with its 4 corners cut off.

For example, hither'southward how yous'd detect the area of EIGHTPLU in the figure below, given that it's a regular octagon with sides of length 6.

The iv corners (similar triangle SUE in the figure) that you cut off the square to turn it into an octagon are 45°- 45°- 90° triangles (you tin testify that to yourself if you experience like it). So all you accept to practice to get the area of the octagon is to summate the area of the square and then subtract the four corner triangles. Piece o' cake.

But first, here are two great tips for this and other issues.

For problems involving regular octagons, 45°- 45°- 90° triangles can come in handy. Add together segments to the diagram to get 1 or more 45°- 45°- ninety° triangles and some squares and rectangles to aid you lot solve the problem.
Think exterior the box. It's easy to get into the habit of looking simply within a figure considering that suffices for the vast majority of issues. But occasionally (similar in this problem), you demand to break out of that rut and look outside the perimeter of the figure.

Okay, so here's what yous exercise. You're given that the octagon's sides have a length of 6. Consider side Eu.

Non just calculate the area of the square and the expanse of a unmarried corner triangle:

To finish, subtract the total expanse of the four corner triangles from the surface area of the square:

Well-nigh This Article

This article is from the book:

Geometry For Dummies ,

About the volume author:

Mark Ryan is the founder and possessor of The Math Center in the Chicago area, where he provides tutoring in all math subjects also as test preparation. Marking is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.