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Intermediate Geometry : Pentagons

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Example Question #13 : How To Find The Length Of The Side Of A Pentagon

If a regular pentagon has an area of and an apothem length of , what is the length of a side of the pentagon?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(50)}{5(10)}=2$

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Example Question #14 : How To Find The Length Of The Side Of A Pentagon

If a regular pentagon has an area of and an apothem of 1.2 , what is the length of a side of the pentagon?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(12)}{5(1.2)}=4$

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Example Question #15 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 20.5 and the length of the apothem is 1.9 , what is the length of a side of the pentagon?

Possible Answers:

6.77

4.32

3.34

5.19

Correct answer:

4.32

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(20.5)}{5(1.9)}=4.32$

Make sure to round to two places after the decimal.

Report an Error

Example Question #16 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 200 and the length of the apothem is 7.1 , what is the length of a side of the pentagon?

Possible Answers:

10.55

11.27

9.52

13.98

Correct answer:

11.27

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(200)}{5(7.1)}=11.27$

Make sure to round to two places after the decimal.

Report an Error

Example Question #17 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is and the length of the apothem is 2.1 , what is the length of a side of the pentagon?

Possible Answers:

10.01

8.45

7.44

9.71

Correct answer:

9.71

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(51)}{5(2.1)}=9.71$

Make sure to round to two places after the decimal.

Report an Error

Example Question #18 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 291 and the length of the apothem is 9.1 , what is the length of a side of the pentagon?

Possible Answers:

12.79

13.01

14.29

11.12

Correct answer:

12.79

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(291)}{5(9.1)}=12.79$

Make sure to round to two places after the decimal.

Report an Error

Example Question #19 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 105 and the length of the apothem is 4.1 , what is the length of a side of the pentagon?

Possible Answers:

12.41

11.95

9.50

10.24

Correct answer:

10.24

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(105)}{5(4.1)}=10.24$

Make sure to round to two places after the decimal.

Report an Error

Example Question #20 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 155 and the length of the apothem is 6.2 , what is the length of a side of the pentagon?

Possible Answers:

12.50

8.75

9.25

Correct answer:

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(155)}{5(6.2)}=10$

Report an Error

Example Question #21 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 512 , and the length of the apothem is 12.5 , what is the length of a side of the pentagon?

Possible Answers:

15.44

16.38

14.29

17.09

Correct answer:

16.38

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(512)}{5(12.5)}=16.38$

Make sure to round to two places after the decimal.

Report an Error

Example Question #22 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 561 , and the length of the apothem is 13.4 , what is the length of a side of the pentagon?

Possible Answers:

15.55

18.29

20.41

16.75

Correct answer:

16.75

Explanation:

Recall how to find the area of a regular pentagon:

$\text{Area}=\frac{1}{2}(\text{apothem})(\text{perimeter})$

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

$\text{perimeter}=5(\text{side})$

Substitute this into the equation for the area.

$\text{Area}=\frac{1}{2}(\text{apothem})(5(\text{side}))$

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

$5(\text{apothem})(\text{side})=2(\text{Area})$

$\text{side}=\frac{2(\text{Area})}{5(\text{apothem})}$

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

$\text{side}=\frac{2(561)}{5(13.4)}=16.75$

Make sure to round to two places after the decimal.

Report an Error

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Intermediate Geometry : Pentagons

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #13 : How To Find The Length Of The Side Of A Pentagon

Example Question #14 : How To Find The Length Of The Side Of A Pentagon

Example Question #15 : How To Find The Length Of The Side Of A Pentagon

Example Question #16 : How To Find The Length Of The Side Of A Pentagon

Example Question #17 : How To Find The Length Of The Side Of A Pentagon

Example Question #18 : How To Find The Length Of The Side Of A Pentagon

Example Question #19 : How To Find The Length Of The Side Of A Pentagon

Example Question #20 : How To Find The Length Of The Side Of A Pentagon

Example Question #21 : How To Find The Length Of The Side Of A Pentagon

Example Question #22 : How To Find The Length Of The Side Of A Pentagon

All Intermediate Geometry Resources

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