# Find the Area of a Rhombus, Each Side of Which Measures 20 Cm and One of Whose Diagonals is 24 Cm. - Mathematics

#### 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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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 20 Mensuration - I (Area of a Trapezium and a Polygon)
Exercise 20.1 | Q 14 | Page 14

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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.