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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 : Rhombuses

A rhombus has an area of 108 square units, an altitude of . Find the perimeter of the rhombus.

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

$A=(base\times altitude)$

$108=(base\times 12)$

$base=108\div12=9$

Then apply the perimeter formula:

P=4S , where is equal to the length of one side of the rhombus.

The solution is:

$P=4\times9=36$

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Example Question #22 : Rhombuses

A rhombus has an area of square units and an altitude of . Find the perimeter of the rhombus.

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

$A=(base\times altitude)$

$56=(base\times 7)$

$base=\frac{56}{7}=8$

Then apply the perimeter formula:

p=4S , where the length of one side of the rhombus.

p=4(8)=32

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Example Question #23 : Rhombuses

Given that a rhombus has an area of 240 square units and an altitude of , find the perimeter of the rhombus.

Possible Answers:

160

Correct answer:

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

$A=(base\times altitude)$

$240=(base\times 16)$

$base=\frac{240}{16}=15$

Then apply the formula: p=4S , where S= 15

p=4(15)=60

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Example Question #24 : Rhombuses

A rhombus has an area of square units and an altitude of 1.8 , find the perimeter of the rhombus.

Possible Answers:

28.5

Correct answer:

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

$A=(base\times altitude)$

$9=(base\times 1.8)$

$base=\frac{9}{1.8}=5$
Then apply the formula: P=4S , where S=5

$P=4\times5=20$

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Example Question #15 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths: and .

Possible Answers:

44.11

45.89

42.52

43.07

Correct answer:

42.52

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{14}{2}=7$

$\frac{\text{Diagonal 2}}{2}=\frac{16}{2}=8$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$7^2+8^2=\text{side length}^2$

$\text{side length}^2=49+64=113$

$\text{side length}=\sqrt{113}$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4\sqrt{113}$

Solve and round to two decimal places.

$\text{Perimeter}=42.52$

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Example Question #16 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths: and

Possible Answers:

21.08

32.66

29.57

28.84

Correct answer:

28.84

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{8}{2}=4$

$\frac{\text{Diagonal 2}}{2}=\frac{12}{2}=6$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$4^2+6^2=\text{side length}^2$

$\text{side length}^2=16+36=52$

$\text{side length}=2\sqrt{13}$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4(2\sqrt{13})$

Solve and round to two decimal places.

$\text{Perimeter}=28.84$

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Example Question #17 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths: and .

Possible Answers:

42.42

42.28

47.05

45.61

Correct answer:

45.61

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{14}{2}=7$

$\frac{\text{Diagonal 2}}{2}=\frac{18}{2}=9$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$7^2+9^2=\text{side length}^2$

$\text{side length}^2=49+81=130$

$\text{side length}=\sqrt{130}$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4(\sqrt{130})$

Solve and round to two decimal places.

$\text{Perimeter}=45.61$

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Example Question #25 : Rhombuses

Find the perimeter of a rhombus if it has diagonals of the following lengths: and .

Possible Answers:

34.77

40.68

Cannot be determined

40.00

Correct answer:

40.00

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{12}{2}=6$

$\frac{\text{Diagonal 2}}{2}=\frac{16}{2}=8$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$6^2+8^2=\text{side length}^2$

$\text{side length}^2=36+64=100$

$\text{side length}=10$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4(10)$

Solve.

$\text{Perimeter}=40$

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Example Question #19 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths: and .

Possible Answers:

73.84

65.29

70.77

71.18

Correct answer:

70.77

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{24}{2}=12$

$\frac{\text{Diagonal 2}}{2}=\frac{26}{2}=13$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$12^2+13^2=\text{side length}^2$

$\text{side length}^2=144+169=313$

$\text{side length}=\sqrt{313}$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4(\sqrt{313})$

Solve and round to two decimal places.

$\text{Perimeter}=70.77$

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Example Question #31 : Rhombuses

Find the perimeter of a rhombus if it has diagonals of the following lengths: and .

Possible Answers:

88.30

89.51

93.08

91.21

Correct answer:

91.21

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{28}{2}=14$

$\frac{\text{Diagonal 2}}{2}=\frac{36}{2}=18$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$14^2+18^2=\text{side length}^2$

$\text{side length}^2=196+324=520$

$\text{side length}=2\sqrt{130}$

Since the sides of a rhombus all have the same length, multiply the side length by in order to find the perimeter.

$\text{Perimeter}=4(\text{side length})$

$\text{Perimeter}=4(2\sqrt{130})$

Solve and round to two decimal places.

$\text{Perimeter}=91.21$

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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 : Rhombuses

Example Question #22 : Rhombuses

Example Question #23 : Rhombuses

Example Question #24 : Rhombuses

Example Question #15 : How To Find The Perimeter Of A Rhombus

Example Question #16 : How To Find The Perimeter Of A Rhombus

Example Question #17 : How To Find The Perimeter Of A Rhombus

Example Question #25 : Rhombuses

Example Question #19 : How To Find The Perimeter Of A Rhombus

Example Question #31 : Rhombuses

All Intermediate Geometry Resources

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