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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Rhombus

Given a rhombus with diagonal lengths of 12cm and 16cm, find the perimeter.

Possible Answers:

$36\;cm$

$24\;cm$

$18\;cm$

$30\;cm$

$40\; cm$

Correct answer:

$40\; cm$

Explanation:

A rhombus is a parallelogram with all of its sides being equal. A square is a rhombus with all of the angles being equal as well as all of the sides. Both squares and rhombuses have perpendicular diagonal bisectors that split each diagonal into 2 equal pieces, and also splitting the quadrilateral into 4 equal right triangles.

With this being said, we know the Pythagorean Theorem would work great in this situation, using half of each diagonal as the two legs of the right triangle.

$\left ( 8 cm \right )^{2}+\left ( 6cm \right )^{2}=h^{2}$ where is the hypotenuse.

$h^{2}=100$ $cm^{2}$ --> h=10cm

We find the hypotenuse to be 10cm. Since the hypotenuse of each triangle is a side of the rhombus, we have found what we need to find the perimeter.

Each side is the same, so we add all 4 sides to find the perimeter.

$10+10+10+10=40\ cm$

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Example Question #1 : How To Find The Perimeter Of A Rhombus

The diagonals of a rhombus have lengths and units. What is its perimeter?

Possible Answers:

$68 \text{ units}$

$32 \text{ units}$

$60 \text{ units}$

$240 \text{ units}$

$46 \text{ units}$

Correct answer:

$68 \text{ units}$

Explanation:

We should begin with a picture.

We should recall several things. First, all four sides of a rhombus are congruent, meaning that if we find one side, we can simply multiply by four to find the perimeter. Second, the diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half. We therefore have four congruent right triangles. Using Pythagorean Theorem on any one of them will give us the length of our sides.

With a side length of 17, our perimeter is easy to obtain.

$\small P=4\cdot17=68$

Our perimeter is 68 units.

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Example Question #11 : 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:

$A=(base\times altitude)$
$42=(base \times 7)$
$base=\frac{42}{7}=6$

Then apply the perimeter formula:

P=4S , where a side of the rhombus.

P=4(6)=24

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Example Question #2 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

14.5

30.5

Correct answer:

Explanation:

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

$A=(base\times altitude)$

$15=(base\times 2)$

$base=\frac{15}{2}=7.5$

Since, perimeter p=4(S) , where is equal to 7.5

Perimeter= $4\times7.5=30$

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Example Question #1 : How To Find The Perimeter Of A Rhombus

A rhombus has a side length of $9\frac{1}{2}$ . Find the perimeter of the rhombus.

Possible Answers:

Correct answer:

Explanation:

To find the perimeter, apply the formula: p=4(S) , where S=9.5

p=4(9.5)=38

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Example Question #1 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

121

Correct answer:

Explanation:

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

$A=(base\times altitude)$

$66=(base\times 6)$

$base=\frac{66}{6}=11$

P=4S , where S=11

P=4(11)=44

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Example Question #7 : How To Find The Perimeter Of A Rhombus

Given that a rhombus has a side length of $4\frac{3}{4}$ , find the perimeter of the rhombus.

Possible Answers:

9.25

19.5

9.5

Correct answer:

Explanation:

To find the perimeter of this rhombus, apply the formula: p=4(S) , where $S=4\frac{3}{4}=\frac{19}{4}$

$P=4(\frac{19}{4})=19$

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Example Question #2 : How To Find The Perimeter Of A Rhombus

A rhombus has an area of 120 square units, and an altitude of 7.5 . 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:

$A=(base\times altitude)$

$120=(base\times 7.5)$

$base=120\div7.5=16$

P=4S , where S=16

P=4(16)=64

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Example Question #9 : How To Find The Perimeter Of A Rhombus

A rhombus has a side length of $\frac{5}{6}$ foot, what is the length of the perimeter (in inches).

Possible Answers:

inches

feet

inches

Correct answer:

inches

Explanation:

To find the perimeter, first convert $\frac{5}{6}$ foot into the equivalent amount of inches. Since, $\frac{5}{6}=\frac{10}{12}$ and $\frac{12}{12}=1foot$ , $\frac{5}{6}$ is equal to inches.

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

Since, S=10

The solution is:

P=4(10)=40

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Example Question #3 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus that has a side length of $6\frac{5}{8}$ .

Possible Answers:

$p=8\div53$

$p=\frac{53}{8}$

$p=\frac{8}{53}$

$p=4(\frac{53}{8})$

$p=\frac{1}{2}$

Correct answer:

$p=4(\frac{53}{8})$

Explanation:

In order to find the perimeter of this rhombus, first convert $6\frac{5}{8}$ from a mixed number to an improper fraction:

$6\frac{5}{8}=\frac{48+5}{8}=\frac{53}{8}$

Then apply the formula: p=4S , where is equal to one side of the rhombus.

Since, $S=\frac{53}{8}$ the solution is:

$p=4(\frac{53}{8})$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Rhombus

Example Question #1 : How To Find The Perimeter Of A Rhombus

Example Question #11 : Rhombuses

Example Question #2 : How To Find The Perimeter Of A Rhombus

Example Question #1 : How To Find The Perimeter Of A Rhombus

Example Question #1 : How To Find The Perimeter Of A Rhombus

Example Question #7 : How To Find The Perimeter Of A Rhombus

Example Question #2 : How To Find The Perimeter Of A Rhombus

Example Question #9 : How To Find The Perimeter Of A Rhombus

Example Question #3 : How To Find The Perimeter Of A Rhombus

All Intermediate Geometry Resources

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