What is the area of a regular pentagon if each side is 2 centimeters?

Answer 1

I believe you can not answer this without knowing the distance from the segment's bisector to the center. If you did, then you would divide the pentagon into 5 triangles and find their areas and add them up.

LOOPDOP says: There IS one method where you only have to know the length (2cm) and the number of sides (5).

Area for ANY regular polygon is

A = 1/4 n x l^2 cot 180/5

Your answer will be:

A = .25 x 5 x 2cm x 2cm x cot 36 degrees

= 5.0 x 1.3764

= 6.8819 square centimeters.

As stated above, you can use this method for any regular polygon where the length and number of sides are known.

From C2H5.OH:

For pentagons, you can also work on the basis of 10 right-angled triangles of the form 36/54/90.

This gives a (simpler?) formula, where S is the side length, of 5 times S squared divided by 4 times the tangent of 36 degrees (call the last bit 2.906 for ease of use!). Your 2cm pentagon works out at 20/2.906 or 6.8823 sqcm, which is as near as makes no difference to the previous answer.