If one side and one diagonal of a rhombus are $5\ cm$ and $8\ cm$ respectively, then find its area in $cm^2$.


Given: One side and one diagonal of a rhombus are $5\ cm$ and $8\ cm$ respectively.

To do: To find its area.

Solution:

Diagonals bisect each other and they are perpendicular in rhombus

Let half the length of second diagonal be $x$.

As two diagonals and a side form right angled triangle,

$\Rightarrow x^2+4^2=5^2$

$\Rightarrow x^2=25-16$

$\Rightarrow x^2=9$

$\Rightarrow x=3$

$\Rightarrow$ Length of 2nd side$=2x=6\ cm$

Area of rhombus$=\frac{1}{2}\times d_1\times d_2$
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$=\frac{1}{2}\times8\times6$

$=24\ cm^2$

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Updated on: 10-Oct-2022

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