A regular pentagon must have five equivalent sides and five equivalent interior angles.

This problem provides the measurement for the total perimeter of the pentagon, work backwards using the formula: 

, where  the length of one side of the pentagon. 

A regular pentagon must have five equivalent sides and five equivalent interior angles. Regular pentagons can be divided up into five equivalent interior triangles, where the base of the triangle is a side length and the height of the triangle is the apothem. This problem provides the total area for the pentagon. 

Therefore, you must work backwards using the area formula: , where the base is equal to the length of one side of the triangle and the height of the triangle is the measurement of the apothem. However, this will only provide the measurement for one of the five interior triangles, thus you first need to divide the total area by 

The solution is:



So, area of one of the five interior triangles is equal to: 

Now, apply the area formula: 

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Make sure to round to two places after the decimal.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Make sure to round to two places after the decimal.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Make sure to round to two places after the decimal.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Make sure to round to two places after the decimal.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.

Make sure to round to two places after the decimal.

Recall how to find the area of a regular pentagon:

Now, the perimeter of a regular pentagon can be found by multiplying the side length by :

Substitute this into the equation for the area.

Now, rearrange the equation to solve for the side length.

Plug in the given area and apothem to solve for the side length of the pentagon.