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

Example Questions

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

A pentagon with perimeter 54 has three congruent sides of length ; its other two sides are congruent to each other. Give the length of each of those other two sides in terms of .

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. If we let  be the length of one of those other two sides, we can set up this equation and solve for :

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

A regular pentagon has perimeter 7 meters. Give the length of one side in millimeters.

Explanation:

One meter is equal to 1,000 millimeters, so the perimeter of 7 meters can be expressed as:

7 meters =  millimeters.

Since the five sides of a regular pentagon are congruent, divide by 5:

millimeters.

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

A regular pentagon has perimeter 42 meters. What is the length of one side in centimeters?

Explanation:

One meter is equal to 100 centimeters, so the perimeter of 42 meters can be expressed as follows:

meters centimeters

In a regular pentagon, all sides are equal in length. Divide the perimeter by 5 to get the length of each side:

centimeters

Example Question #4 : How To Find The Perimeter Of A Pentagon

The perimeter of a pentagon is . The pentagon has three congruent sides of length meters. Its other two sides are congruent to each other, each with a length of .

Find .

Explanation:

The perimeter of a polygon is sum of the lengths of its sides. In this pentagon, three sides have the same length of 4 and two others have the same length of . So we can write:

Now we should solve this equation for :

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

A pentagon with perimeter 40 meters has two congruent sides of length . Its other three sides are congruent to each other. Give the length of each of the other three sides in terms of .

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. Let:

length of one of those other three sides

Now we have:

So the length of each of those other three sides is

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

Two sides of a pentagon have a length of , and three other sides have the length of . Give the perimeter of the pentagon in terms of .

Explanation:

The perimeter of a polygon is the sum of the lengths of its sides. So we can write:

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

Each exterior angle of a pentagon is 72 degrees and the length of one side is 4 meters. Give the perimeter of the pentagon.

Explanation:

As each exterior angle of the pentagon is 72 degrees, each interior angle would be

That means all of the interior angles of the pentagon are identical, so we have a regular pentagon.

The perimeter of a polygon is the sum of the lengths of its sides. So the perimeter of a regular pentagon is ; where is the length of a side.

So we get:

meters

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

A pentagon has four congruent sides of length . The length of the fifth side is meters.

Give the perimeter of the pentagon.