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ACT Math : How to find the area of a rhombus

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Example Question #11 : How To Find The Area Of A Rhombus

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

Possible Answers:

$72\:cm^2$ $\displaystyle 72\:cm^2$

$54\:cm^2$ $\displaystyle 54\:cm^2$

$96\:cm^2$ $\displaystyle 96\:cm^2$

$88\:cm^2$ $\displaystyle 88\:cm^2$

$36\:cm^2$ $\displaystyle 36\:cm^2$

Correct answer:

$36\:cm^2$ $\displaystyle 36\:cm^2$

Explanation:

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

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

where $\displaystyle p$ and $\displaystyle q$ 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:

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

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

$A= 36\:cm^2$ $\displaystyle A= 36\:cm^2$

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Example Question #11 : Geometry

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

Possible Answers:

$800\:cm^2$ $\displaystyle 800\:cm^2$

$600\:cm^2$ $\displaystyle 600\:cm^2$

$200\:cm^2$ $\displaystyle 200\:cm^2$

$400\:cm^2$ $\displaystyle 400\:cm^2$

$900\:cm^2$ $\displaystyle 900\:cm^2$

Correct answer:

$400\:cm^2$ $\displaystyle 400\:cm^2$

Explanation:

Write the formula for the area of a rhombus:

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

Substitute the given lengths of the diagonals and solve:

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

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

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

Possible Answers:

5a^3 $\displaystyle 5a^3$

2a+5a^2 $\displaystyle 2a+5a^2$

7a^3 $\displaystyle 7a^3$

5a^2 $\displaystyle 5a^2$

10a^3 $\displaystyle 10a^3$

Correct answer:

5a^3 $\displaystyle 5a^3$

Explanation:

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

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

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ACT Math : How to find the area of a rhombus

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : How To Find The Area Of A Rhombus

Example Question #11 : Geometry

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

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