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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$=\frac{1}{2}\times d_1\times d_2$
$=\frac{1}{2}\times8\times6$
$=24\ cm^2$
Updated on: 10-Oct-2022
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