Question

Find the area of a rhombus whose side is $6cm$ and whose altitude is $4cm$. If one of its diagonal is $8cm$ long, find the length of the other diagonal.

Answer 1

Step 1 : Find the area of the rhombus

Given: Dimensions of rhombus:
Side = $6cm$, Altitude $=4cm$

Since, area of rhombus $=$ side $\times$ Altitude
$=6\times 4$
$=24c{m}^2$

Therefore, area of the rhombus is $24c{m}^2.$

Step 2: Find the other diagonal

Given: One of the diagonal $\left(d_1\right)$ is $8cm$ and area of the rhombus = $24c{m}^2$

We know that,
Area of rhombus $=\frac{1}{2}\times (d_1\times d_2)$
where $d_{1}and{d}_2$ are diagonals
$\Rightarrow 24=\frac{1}{2}\times 8\times d_2$

$\Rightarrow d_2=6cm$

Thus, the length of the other diagonal is $6cm$.

Hence, area of the rhombus is $24c{m}^2$ and the length of the other diagonal is $6cm$.