How to find the area of a regular pentagon formula

Asked by admin @ in Mathematics viewed by 294 People

What is the area of regular pentagon with a side of 12 inches? Round the answer to the nearest 10th.

Answered by admin @


The area would be 247.8 sq. in.

We start out finding the length of the apothem.  The apothem of a regular polygon is given by 

A=\frac{s}{2\tan{(\frac{180}{n})}}

where s is the side length and n is the number of sides.  Using our information, we have
A=\frac{5}{2\tan{(\frac{180}{5})}}=\frac{5}{2\tan{36}}=8.26

Now we find the area of the polygon using the formula:
A = n(1/2)(b)(h), where n is the number of sides, b is the side length, and h is the length of the apothem:

A = 5(1/2)(8.26)(12) = 247.8

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