#### Question

Find the area of a rhombus, each side of which measures 20 cm and one of whose diagonals is 24 cm.

Sum

#### Solution

Given:

Side of the rhombus = 20 cm

Length of a diagonal = 24 cm

We know: If `d_1` and `d_2` are the lengths of the diagonals of the rhombus, then

side of the rhombus\[= \frac{1}{2}\sqrt{d_1^2 + d_2^2}\]

So, using the given data to find the length of the other diagonal of the rhombus:

\[20 = \frac{1}{2}\sqrt{{24}^2 + d_2^2}\]

\[40 = \sqrt{{24}^2 + d_2^2}\]

Squaring both sides to get rid of the square root sign:

\[ {40}^2 = {24}^2 + d_2^2 \]

\[ d_2^2 =1600-576=1024\]

\[ d_2 =\sqrt{1024}=32 cm\]

∴ Area of the rhombus \[=\frac{1}{2}(24 \times 32) = 384 {cm}^2\]

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Find the Area of a Rhombus, Each Side of Which Measures 20 Cm and One of Whose Diagonals is 24 Cm. Concept: Area of a Polygon.

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