Question

Area of square ABCD is 400 $c{m}^2$. Find the area of rhombus PQRS.

• A. 400 $c{m}^2$
• B. 200 $c{m}^2$
• C. 100 $c{m}^2$
• D. 800 $c{m}^2$

Answer 1

The correct option is B 200 $c{m}^2$

Given
Area of square = 400 $c{m}^2$

We know that
Area of square = $sid{e}^2$

$\Rightarrow sid{e}^2$ = 400
$\Rightarrow$ Side of the square = 20 cm

Area of rhombus = $\frac{1}{2}\times$(product of diagonals)

From the figure, we can observe that
the length of side of squares is equal to length of diagonals of rhombus.
i.e, PR = AD = 20 cm and
SQ = AB = 20 cm
Area of rhombus = $\frac{1}{2}$$\times$ $PR\times SQ$
= $\frac{1}{2}\times 20\times 20$
= 200 cm${}^2$

Therefore, area of the rhombus = 200 cm${}^2$