High School Math : How to find the length of the side of a pentagon

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #5 : Pentagons

What is the side length of a regular pentagon with a perimeter of \(\displaystyle 80\)?

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle 12\)

\(\displaystyle 40\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 16\)

Explanation:

To find the side length of a regular pentagon with a perimeter of \(\displaystyle 80\) you must use the equation for the perimeter of a pentagon.

The equation is \(\displaystyle Perimeter=(side\: length)*(number\: ofsides)\)

Plug in the numbers for perimeter and number of sides to get \(\displaystyle 80=(side\: length)*(5)\)

Divide each side of the equation by the number of sides to get the answer for the side length. \(\displaystyle \frac{80}{5}=\frac{(side\: length)*(5)}{5}\)

The answer is \(\displaystyle \frac{80}{5}=16\).

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

Find the length of the side of the following pentagon.

Angle_length_of_side_pentagon

The perimeter of the pentagon is \(\displaystyle 30\ m\).

Possible Answers:

\(\displaystyle 7\ m\)

\(\displaystyle 4\ m\)

\(\displaystyle 8\ m\)

\(\displaystyle 6\ m\)

 

 

 

\(\displaystyle 5\ m\)

Correct answer:

\(\displaystyle 6\ m\)

 

 

 

Explanation:

The formula for the perimeter of a regular pentagon is

\(\displaystyle P = 5(s)\),

where \(\displaystyle s\) represents the length of the side.

Plugging in our values, we get:

\(\displaystyle 30\ m=5(s)\)

\(\displaystyle s=6\ m\)

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

Find the length of the side of the following pentagon.

Angle_length_of_side_pentagon

The perimeter of the pentagon is \(\displaystyle 20\ m\).

Possible Answers:

\(\displaystyle 3\ m\)

\(\displaystyle 7\ m\)

\(\displaystyle 9\ m\)

\(\displaystyle 4\ m\)

\(\displaystyle 5\ m\)

 

 

 

Correct answer:

\(\displaystyle 4\ m\)

Explanation:

The formula for the perimeter of a regular pentagon is

\(\displaystyle P = 5(s)\),

where \(\displaystyle s\) represents the length of the side.

Plugging in our values, we get:

\(\displaystyle 20\ m = 5(s)\)

\(\displaystyle s=4\ m\)

 

 

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