How to find the area of a pentagon Flashcards - GRE Quantitative Reasoning

The formula for the area of a regular pentagon is given by the equation:

$A=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is represented by the length of one side. Let's begin by finding the side length of the regular pentagon. If the perimeter is 40, then we can divide by 5 (the number of sides) to find a side length of 8.

If we plug in 8 into the equation:

$A=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}(8)^2$

$A=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}64$

$A=\frac{64}{4}\sqrt{5(5+2\sqrt{5})}$

$A=16\sqrt{5(5+2\sqrt{5})}$

How to find the area of a pentagon - GRE Quantitative Reasoning

The perimeter of a regular pentagon is 40 units. What is the area of the pentagon?