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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon.

Possible Answers:

112

132

Correct answer:

Explanation:

When all the opposite sides of a regular hexagon are connected, you should notice that six congruent equilateral triangles are created:

Thus, the diagonal of the hexagon is twice the length of a side.

$\text{Diagonal}=2(\text{side})$

$\text{Side}=\frac{\text{Diagonal}}{2}$

Plug in the given diagonal to find the length of a side.

$\text{Side}=\frac{22}{2}=11$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter.

$\text{Perimeter}=6(11)=66$

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Example Question #22 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is , what is the perimeter of the hexagon?

Possible Answers:

13.21

14.42

14.33

15.80

Correct answer:

14.42

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(15)}{3\sqrt3}}=14.42$

Make sure to round to the two places after the decimal.

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Example Question #21 : Hexagons

If the area of a regular hexagon is $15\sqrt3$ , what is the perimeter of the hexagon?

Possible Answers:

20.51

18.97

19.82

16.58

Correct answer:

18.97

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(15\sqrt3)}{3\sqrt3}}=18.97$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #24 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is , what is the perimeter of the hexagon?

Possible Answers:

19.14

18.61

18.12

17.78

Correct answer:

18.61

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(25)}{3\sqrt3}}=18.61$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #25 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is , what is the perimeter of the hexagon?

Possible Answers:

32.31

22.95

28.88

29.01

Correct answer:

22.95

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(38)}{3\sqrt3}}=22.95$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #26 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is 178 , what is the perimeter of the hexagon?

Possible Answers:

51.09

41.29

45.51

49.66

Correct answer:

49.66

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(178)}{3\sqrt3}}=49.66$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #27 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is 109 , what is the perimeter of the hexagon?

Possible Answers:

35.77

32.01

38.86

41.12

Correct answer:

38.86

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(109)}{3\sqrt3}}=38.86$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #28 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is 120 , what is the perimeter of the hexagon?

Possible Answers:

40.78

45.12

50.69

39.51

Correct answer:

40.78

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(120)}{3\sqrt3}}=40.78$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #29 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is 219 , what is the perimeter of the hexagon?

Possible Answers:

56.69

55.09

81.24

61.20

Correct answer:

55.09

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(219)}{3\sqrt3}}=55.09$

Make sure to round to the two places after the decimal.

Report an Error

Example Question #30 : How To Find The Perimeter Of A Hexagon

If the area of a regular hexagon is 456 , what is the perimeter of the hexagon?

Possible Answers:

75.39

79.49

74.13

71.21

Correct answer:

79.49

Explanation:

Recall the formula to find the area of a regular hexagon:

$\text{Area}=\frac{3\sqrt3}{2}(\text{side})^2$

Rearrange the formula to solve for the side.

$(\text{side})^2=\text{Area}(\frac{2}{3\sqrt3})$

$\text{side}=\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Now, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Substitute in for the side to solve for the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(\text{Area})}{3\sqrt3}}$

Plug in the given area and use a calculator to find the perimeter.

$\text{Perimeter}=6\sqrt{\frac{2(456)}{3\sqrt3}}=79.49$

Make sure to round to the two places after the decimal.

Report an Error

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #21 : How To Find The Perimeter Of A Hexagon

Example Question #22 : How To Find The Perimeter Of A Hexagon

Example Question #21 : Hexagons

Example Question #24 : How To Find The Perimeter Of A Hexagon

Example Question #25 : How To Find The Perimeter Of A Hexagon

Example Question #26 : How To Find The Perimeter Of A Hexagon

Example Question #27 : How To Find The Perimeter Of A Hexagon

Example Question #28 : How To Find The Perimeter Of A Hexagon

Example Question #29 : How To Find The Perimeter Of A Hexagon

Example Question #30 : How To Find The Perimeter Of A Hexagon

All Intermediate Geometry Resources

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