A rhombus has diagonals that measure $6\ cm$ and $8\ cm$. What is its area? How much does each side measure?

Given: A rhombus has diagonals that measure $6\ cm$ and $8\ cm$

To do: To find its area and measure of each side.

Solution:

As given, diagonals of the rhombus $d_{1}=6\ cm$ and $d_{2}=8\ cm$

Area of rhombus $A= \frac{( d_1\times d_2)}{2}$

                                   $= \frac{(6 \times  8)}{2}$

                                   $= \frac{48}{2}$

                                   $= 24\ cm^2$

        Side $= \sqrt{( \frac{d_1}{2})^2 + (\frac{d_2}{2})^2}$

                $=\sqrt{  ( \frac{6}{2})^2 + (\frac{8}{2})^2}$

                $= \sqrt{  3^2 + 4^2}$

                $= \sqrt{  9 + 16}$

                $= \sqrt{  25}$

                $= 5\ cm$
 

Updated on: 10-Oct-2022

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