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

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Example Questions

Example Question #753 : Plane Geometry

A regular pentagon has a perimeter of $\small 125$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 35$

$\small 25$

$\small 20$

$\small 75$

$\small 15$

Correct answer:

$\small 25$

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:

$\small p=5(s)$ , where $\small s =$ the length of one side of the pentagon.

$\small 125=5(s)$

$\small s=\frac{125}{5}=25$

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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 $\small \small 75$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 20$

$\small 5$

$\small 12$

$\small 25$

$\small 15$

Correct answer:

$\small 15$

Explanation:

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

A regular pentagon has an area of $\small 80$ square units and an apothem measurement of $\small 4.7$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 16$

$\small 4.3$

$\small 6.8$

$\small 4.2$

$\small 8.6$

Correct answer:

$\small 6.8$

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: $\small a=\frac{base\times height}{2}$ , 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 $\small 5.$

The solution is:

$\small a=80$

So, area of one of the five interior triangles is equal to: $\small 80\div5=16$

Now, apply the area formula:

$\small 16=\frac{base\times 4.7}{2}$

$\small 32=base\times4.7$

$\small base=32\div4.7=6.8$

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

A regular pentagon has an area of $\small 32.5$ square units and an apothem measurement of $\small \small 3$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 3.9$

$\small 4.3$

$\small 3.4$

$\small 2.9$

$\small 5.3$

Correct answer:

$\small 4.3$

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: $\small a=\frac{base\times height}{2}$ , 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 $\small 5.$

The solution is:

$\small \small a=32.5$

So, area of one of the five interior triangles is equal to: $\small \small 32.5\div5=6.5$

Now, apply the area formula:

$\small \small 6.5=\frac{base\times 3}{2}$

$\small \small 13=base\times3$

$\small \small base=13\div3=4.3$

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

Pentagon_series_vt_custom

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 $\small x.$

Possible Answers:

$\small 8.5$

$\small 6.25$

$\small 12$

$\small 8.25$

$\small 12.5$

Correct answer:

$\small 12$

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:

$\small a=width\times length$

$\small \small 174=14.5\times x$

$\small x=174\div14.5=12$

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

A regular pentagon has a perimeter of $\small \small 225$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 40$

$\small 30$

$\small 35$

$\small 45$

$\small 55$

Correct answer:

$\small 45$

Explanation:

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

A regular pentagon has an area of $\small \small 180$ square units and an apothem measurement of $\small \small 7$ . Find the length of one side of the pentagon.

Possible Answers:

$\small \small 10.3$

$\small 8.9$

$\small 10.9$

$\small 6.25$

$\small 7.25$

Correct answer:

$\small \small 10.3$

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: $\small a=\frac{base\times height}{2}$ , 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 $\small 5.$

The solution is:

$\small \small a=180$

So, area of one of the five interior triangles is equal to: $\small \small 180\div5=36$

Now, apply the area formula:

$\small \small 36=\frac{base\times 7}{2}$

$\small \small 72=base\times7$

$\small \small base=72\div 7=10.3$

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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 $\small \small \small 64$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 9.25$

$\small 8.8$

$\small 12.8$

$\small 12$

$\small 10.7$

Correct answer:

$\small 12.8$

Explanation:

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

A regular pentagon has an area of $\small \small 156$ square units and an apothem measurement of $\small \small 6.6$ . Find the length of one side of the pentagon.

Possible Answers:

$\small 6.9$

$\small \small 9.5$

$\small 7.25$

$\small 6.6$

$\small 9.9$

Correct answer:

$\small \small 9.5$

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: $\small a=\frac{base\times height}{2}$ , 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 $\small 5.$

The solution is:

$\small \small a=156$

So, area of one of the five interior triangles is equal to: $\small \small 156\div5=31.2$

Now, apply the area formula:

$\small \small 31.2=\frac{base\times 6.6}{2}$

$\small \small 62.4=base\times6.6$

$\small \small base=62.4\div 6.6= 9.5$

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

Pentagon_series_vt_custom

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 $\small x.$

Possible Answers:

$\small 8.5$

$\small 7.25$

$\small 6.25$

$\small 6.5$

$\small 5.5$

Correct answer:

$\small 5.5$

Explanation:

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

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #753 : Plane Geometry

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

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

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

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

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

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

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

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

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

All Intermediate Geometry Resources

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