# SSAT Upper Level Math : How to find the area of a pentagon

## Example Questions

### Example Question #1 : How To Find The Area Of A Pentagon

Find the exact area of a pentagon if the side length is .

Explanation:

Write the formula for the area of a pentagon.

Substitute the side length and simplify.

### Example Question #2 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of  and an apothem of .

Explanation:

To find the area of a regular polygon,

To find the perimeter of the pentagon,

For the given pentagon,

So then, to find the area of the pentagon,

### Example Question #3 : How To Find The Area Of A Pentagon

Find the area of a regular pentagon that has a side length of  and an apothem of .

Explanation:

To find the area of a regular polygon,

To find the perimeter of the pentagon,

For the given pentagon,

So then, to find the area of the pentagon,

### Example Question #21 : Areas And Perimeters Of Polygons

Find the area of a regular pentagon with a side length of .

Explanation:

Use the following formula to find the area of a regular pentagon:

Plugging in the information given by the question,

### Example Question #5 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of  and an apothem of .

Explanation:

To find the area of a regular polygon,

To find the perimeter of the pentagon,

For the given pentagon,

So then, to find the area of the pentagon,

### Example Question #6 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of  and an apothem of .

Explanation:

To find the area of a regular polygon,

To find the perimeter of the pentagon,

For the given pentagon,

So then, to find the area of the pentagon,

### Example Question #7 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of  and an apothem of .

Explanation:

To find the area of a regular polygon,

To find the perimeter of the pentagon,

For the given pentagon,

So then, to find the area of the pentagon,

### Example Question #8 : How To Find The Area Of A Pentagon

The area of a regular polygon is . If the length of its apothem is , what is the length of each side of the pentagon?

Explanation:

To find the area of a regular polygon,

For the given pentagon,

To find the length of each side of the pentagon, divide the perimeter by .

### Example Question #9 : How To Find The Area Of A Pentagon

A regular pentagon has an area of . Find the length of each side of the pentagon if the apothem has a length of .

Explanation:

To find the area of a regular polygon,

For the given pentagon,

To find the length of each side of the pentagon, divide the perimeter by .

### Example Question #1 : How To Find The Area Of A Pentagon

The area of a regular pentagon is . Find the length of a side of the pentagon if the apothem has a length of .