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

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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.

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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.

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Example Question #23 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 274 , and the length of the apothem is 6.9 , what is the length of the side of the pentagon?

Possible Answers:

14.29

15.88

13.44

20.59

Correct answer:

15.88

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.

$\text{side}=\frac{2(274)}{5(6.9)}=15.88$

Make sure to round to two places after the decimal.

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Example Question #24 : How To Find The Length Of The Side Of A Pentagon

If the area of a regular pentagon is 306 , and the length of the apothem is 7.4 , what is the length of a side of the pentagon?

Possible Answers:

14.41

17.02

15.89

16.54

Correct answer:

16.54

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.

$\text{side}=\frac{2(306)}{5(7.4)}=16.54$

Make sure to round to two places after the decimal.

Report an Error

Example Question #25 : How To Find The Length Of The Side Of A Pentagon

In pentagon ABCDE , if the length of is one-fifth the length of , what is the length of the side ?

Possible Answers:

57.48

63.11

49.80

51.42

Correct answer:

51.42

Explanation:

Notice that this pentagon is made up of one rectangle and two right triangles. In order to find the length of , we will first need to find the length of .

Let be the length of , so then the length of can be represented by .

Since we have rectangle ABCD , we know that AD=BC .

Thus, AF+FD=AD=60

Now, plug in the variables and solve for .

x+5x=60

6x=60

x=10

Thus, we know that $AF=10\text{ and }FD=50$ .

Now, use the Pythagorean theorem to find the length of .

$ED=\sqrt{(EF)^2+(FD)^2}$

$ED=\sqrt{12^2+50^2}=51.42$

Make sure to round to places after the decimal.

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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 #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

Example Question #23 : How To Find The Length Of The Side Of A Pentagon

Example Question #24 : How To Find The Length Of The Side Of A Pentagon

Example Question #25 : How To Find The Length Of The Side Of A Pentagon

All Intermediate Geometry Resources

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