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ACT Math : Quadrilaterals

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

If the area of a rhombus is $60\:cm^2$ , and the length of one of its diagonals is $2\:cm$ , what must be the length of the other diagonal?

Possible Answers:

$90\:cm$

$45\:cm$

$120\:cm$

$60\:cm$

$30\:cm$

Correct answer:

$60\:cm$

Explanation:

Write the formula for the area of a rhombus.

$A=\frac{d_1\cdot d_2}{2}$

Plug in the given area and diagonal length. Solve for the other diagonal.

$60\:cm^2=\frac{2\:cm\cdot d_2}{2}$

$2(60\:cm^2)=2(\frac{2\:cm\cdot d_2}{2})$

$120\:cm^2=2\:cm\cdot d_2$

$\frac{120\:cm}{2\:cm}=\frac{2\:cm\cdot d_2}{2\:cm}$

$d_2 =60\:cm$

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Example Question #101 : Quadrilaterals

A rhombus contains diagonals with the length $12 \:cm$ and $6 \:cm$ . Find the area of the rhombus.

Possible Answers:

$96\:cm^2$

$88\:cm^2$

$36\:cm^2$

$72\:cm^2$

$54\:cm^2$

Correct answer:

$36\:cm^2$

Explanation:

The equation for the area of a rhombus is given by:

$A= \frac{p \cdot q}{2}$

where and are the two diagonal lengths.

This problem very quickly becomes one of the "plug and chug" type, where the given values just need to be substituted into the equation and the equation then solved. By plugging in the values given, we get:

$A = \frac{12\:cm \cdot 6\:cm}{2}$

$A = \frac{72\:cm^2}2{}$

$A= 36\:cm^2$

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Example Question #15 : Rhombuses

Find the area of a rhombus if the diagonals lengths are $20\:cm$ and $40\:cm$ .

Possible Answers:

$800\:cm^2$

$400\:cm^2$

$900\:cm^2$

$600\:cm^2$

$200\:cm^2$

Correct answer:

$400\:cm^2$

Explanation:

Write the formula for the area of a rhombus:

$A=\frac{d_1 \cdot d_2}{2}$

Substitute the given lengths of the diagonals and solve:

$A=\frac{d1 \cdot d2}{2} = \frac{20\:cm \cdot 40\:cm}{2} =\frac{800\:cm^2}{2} = 400\:cm^2$

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Example Question #11 : Geometry

Find the area of a rhombus if the diagonals lengths are and 5a^2 .

Possible Answers:

5a^3

5a^2

7a^3

10a^3

2a+5a^2

Correct answer:

5a^3

Explanation:

Write the formula for finding the area of a rhombus. Substitute the diagonals and evaluate.

$A=\frac{d1\cdot d2}{2}= \frac{2a \cdot 5a^2}{2}= 5a^3$

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Example Question #451 : Plane Geometry

If a side length of a rhombus is half, what is the perimeter of the rhombus?

Possible Answers:

$\frac{\sqrt2}{2}$

$\frac{1}{8}$

Correct answer:

Explanation:

Write the formula to find the perimeter of a rhombus.

P=4s

Substitute the side length and simplify.

$P=4(\frac{1}{2})=2$

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

Find the perimeter of a rhombus if the side length is .

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the perimeter of a rhombus.

P=4s

Substitute the side length and solve.

P=4(9)=36

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

If the side length of a rhombus is $\frac{11}{8}a+\frac{1}{2}b$ , what is the perimeter?

Possible Answers:

$\frac{11}{2}a+2b$

$\frac{11}{8}a^4+\frac{1}{2}b^4$

$\frac{11}{8}a^2+\frac{1}{2}b^2$

4a+4b

$\frac{32}{11}a+\frac{1}{8}b$

Correct answer:

$\frac{11}{2}a+2b$

Explanation:

Write the formula for the perimeter of a rhombus.

P=4s

Substitute the side length and solve for the perimeter.

$P=4\left(\frac{11}{8}a+\frac{1}{2}b\right) = \frac{11}{2}a+2b$

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

If the diagonals of a rhombus were and , what is the side length of the rhombus?

Possible Answers:

$\frac{\sqrt3}{4}$

$2\sqrt5$

$\frac{\sqrt5}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{\sqrt5}{2}$

Explanation:

Write the formula used to find the rhombus side length given 2 diagonals.

$s = \frac{\sqrt{(d1)^2+(d2)^2}}{2}$

Substitute both diagonals in the equation and simplify.

$s = \frac{\sqrt{(1)^2+(2)^2}}{2}=\frac{\sqrt{1+4}}{2}= \frac{\sqrt5}{2}$

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

A rhombus has a perimeter of 114 . Find the length for one side of the rhombus.

Possible Answers:

$24\frac{1}{4}$

24.5

28.25

28.5

Correct answer:

28.5

Explanation:

To solve this problem, apply the perimeter formula for a rhombus: P=4S .
By applying the perimeter formula, the solution is:

114=4(s)

$s=\frac{114}{4}=28.5$

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

Rhombus custom vt

Using the rhombus shown above, find the length of side .

Possible Answers:

63.25

58.25

63.5

69.5

Correct answer:

69.5

Explanation:

The perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have equivalent sides. Thus, the total perimeter is the sum of all sides.

To solve this problem, apply the perimeter formula for a rhombus: P=4S .
By applying the perimeter formula, the solution is:

278=4(s)

$s=278\div4=69.5$

Check:

$69.5\times4=278$

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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #101 : Quadrilaterals

Example Question #15 : Rhombuses

Example Question #11 : Geometry

Example Question #451 : Plane Geometry

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

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

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

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

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

All ACT Math Resources

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