Intermediate Geometry : How to find the length of the side of a pentagon

Example Questions

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

A regular pentagon has a perimeter of . Find the length of one side of the pentagon.

Explanation:

By definition a regular pentagon must have five equivalent sides and five equivalent interior angles. Since 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.

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

A regular pentagon has a perimeter of . Find the length of one side of the pentagon.

Explanation:

By definition a regular pentagon must have five equivalent sides and five equivalent interior angles. Since 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.

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

A regular pentagon has an area of  square units and an apothem measurement of . Find the length of one side of the pentagon.

Explanation:

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:

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

A regular pentagon has an area of  square units and an apothem measurement of . Find the length of one side of the pentagon.

Explanation:

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:

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

The pentagon shown above has been divided into a top portion with two equivalent right triangles and a bottom rectangular portion. Find the length of side

Explanation:

To solve this problem notice that the area is provided for the bottom rectangular portion of the pentagon. Therefore, work backwards using the area formula:

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

A regular pentagon has a perimeter of . Find the length of one side of the pentagon.

Explanation:

By definition a regular pentagon must have five equivalent sides and five equivalent interior angles. Since 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.

Check:

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

A regular pentagon has an area of  square units and an apothem measurement of . Find the length of one side of the pentagon.

Explanation:

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:

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

A regular pentagon has a perimeter of . Find the length of one side of the pentagon.

Explanation:

By definition a regular pentagon must have five equivalent sides and five equivalent interior angles. Since 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.

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

A regular pentagon has an area of  square units and an apothem measurement of . Find the length of one side of the pentagon.

Explanation:

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:

Example Question #10 : How To Find The Length Of The Side Of A Pentagon

The pentagon shown above has been divided into a top portion with two equivalent right triangles and a bottom rectangular portion. Find the length of side

Explanation:

To solve this problem notice that the area is provided for the bottom rectangular portion of the pentagon. Therefore, work backwards using the area formula:

CHECK:

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