- From: James Pallett
- Date: 12 March 1999
*Subject: Area of a Pentagon*
I am wondering how to find the area of a Regular Pentagon. I need to be able to do this for my GCSE coursework on areas of shapes with fixed perimeters. |

When finding areas, we suggest you break your shape into 'easy' shapes:

- Rectangles;
- Triangles;
- Circles;
- and any other shapes whose area you
*can*calculate.

Suppose the pentagon has each side of length 10 cm.

In this case, you can split the regular pentagon into 5 identical triangles.

The area of the pentagon is five times the area of one triangle:

- The angle
*A*is 360° ÷ 5 = 72°. - Angle
*B*is half of that, 36°. - In the right-angled triangle that includes angle
*B*, 'opp'=5cm and 'adj'=*h*:

- Area of each of the five 'green' triangles is:

- So the area of the pentagon is 5×34.4 =
**172cm²**

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