Find the area of a regular decagon with perimeter 100 units. Show all work.

A regular polygon has ten (10) equal sides (since it is regular).

We are given with the perimeter value which is 100 units and the perimeter formula is P = 10a

Solving for a (the side measurement), we have:

100 = 10a

a = 100/10

a = 10

We can now proceed in solving the area and the formula is shown below:

Area = 5/2 a√ (5+2√5)

Area = 5/2 * 10√ (5+2√5)

Area = 76.94 square units

The answer is 96.94 square units.