How to find the area of a rhombus - ACT Math

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Question

A rhombus contains diagonals with the length and . Find the area of the rhombus.

Answer

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:

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

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

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Question

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

Answer

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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Question

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

Answer

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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