Question

Calculate the area of the regular pentagon below:

A regular pentagon with side length of 11.8 inches and dotted line from center to middle of side of 8.1 inches.

Answer 1

238.95 in²

Explanation:

The area is that of 5 triangles of the given dimensions. Each triangle has an area of ...

A = 1/2bh = 1/2(11.8 in)(8.1 in) = 47.79 in²

Then the area of the pentagon is ...

pentagon area = 5 × 47.79 in² = 238.95 in²

_____

The formula is often written as ...

A = 1/2Pa

where P is the perimeter (5 times the side length) and "a" is the apothem, the distance from the center to the middle of one side. This gives you the same result.