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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

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

Possible Answers:

5a^3

10a^3

5a^2

7a^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 #1 : How To Find The Perimeter Of A Rhombus

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 #2 : 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:

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

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

4a+4b

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

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

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:

$2\sqrt5$

$\frac{3}{2}$

$\frac{\sqrt3}{4}$

$\frac{\sqrt5}{2}$

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 #1 : 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 #1 : 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

63.5

58.25

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

Rhombus custom vt

A rhombus has two perpendicular interior diagonal lines. The diagonals have lengths of and . Find the length for side .

Possible Answers:

12.5

9.5

24.5

Correct answer:

12.5

Explanation:

This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:

$s=\frac{\sqrt{a^2+b^2}}{2}$

where the length of one side, and both and each represent one of the perpendicular diagonal lines.

The solution is:

$s=\frac{\sqrt{15^2+20^2}}{2}=\frac{\sqrt{225+400}}{2}=\frac{\sqrt{625}}{2}=\frac{25}{2}=12.5$

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

The perimeter of a rhombus is equal to $\sqrt{64}$ . Find the length for one side of the rhombus.

Possible Answers:

4.5

$\sqrt{8}$

Correct answer:

Explanation:

To solve this problem, apply the perimeter formula for a rhombus: P=4S .
Note that 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. The total perimeter is the sum of all sides.

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.

By applying the perimeter formula, the solution is:

$\sqrt{64}=4(s)$

8=4(s)

$s=\frac{8}{4}=2$

Check:

$\sqrt{64}=4(2)$

8=8

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

A rhombus has two perpendicular interior diagonal lines, each with endpoints that are the vertex of opposite interior angles. The diagonals have lengths of and . Find the length for one side of the rhombus.

Possible Answers:

5.5

2.5

4.25

2.25

Correct answer:

2.5

Explanation:

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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

Example Question #2 : 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 #1 : How To Find The Length Of The Side Of A Rhombus

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

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

All ACT Math Resources

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