# Intermediate Geometry : How to find the area of a pentagon

## Example Questions

### Example Question #11 : How To Find The Area Of A Pentagon

Find the area of the pentagon shown above.

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Explanation:

To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:

The area of the two right triangles can be found using the formula:

Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.

Thus, the solution is:

### Example Question #12 : How To Find The Area Of A Pentagon

A regular pentagon has a perimeter of  and an apothem length of . Find the area of the pentagon.

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Explanation:

To solve this problem, first work backwards using the perimeter formula for a regular pentagon:

Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have  equal sides and  equivalent interior angles.

This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into  equivalent interior triangles. Each triangle will have a base of  and a height of

The area of this pentagon can be found by applying the area of a triangle formula:

Thus, the area of the entire pentagon is:

### Example Question #13 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

None of these

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #14 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #15 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #16 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #17 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #18 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #19 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.

Explanation:

Recall that the area of regular polygons can be found using the following formula:

First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:

Substitute in the length of the given side of the pentagon in order to find the perimeter.

Next, substitute in the given and calculated information to find the area of the pentagon.

### Example Question #20 : How To Find The Area Of A Pentagon

Find the area of the regular pentagon.