Question

Construct a rhombus of side $6cm$ and one diagonal of length $10cm$. The area of the rhombus is:

• A. $33c{m}^2$
• B. $44c{m}^2$
• C. $55c{m}^2$
• D. $66c{m}^2$

Answer 1

The correct option is A $33c{m}^2$

$\Rightarrow$ We know that all the sides of the rhombus are equal. We have given side is 6cm and ine diagonal is 10cm.

$\Rightarrow$ Draw an line segment PQ = 6cm.

$\Rightarrow$ Take P as a center with radius 10cm and draw an arc.

$\Rightarrow$ Take Q as a center with radius 6cm and draw an arc, meeting previous arc at point R.

$\Rightarrow$ Take P as a center with radius 6cm and draw an arc.

$\Rightarrow$ Take R as a center with radius 6cm and draw an arc meeting previous arc at point S.

$\Rightarrow$ Join PR, QR, RS, PS and QS.

$\Rightarrow$ Measure the length of two diagonal AP and QS

$\Rightarrow$ We get, $l\left(PR\right)=10cm,l\left(QS\right)=6.6cm$

$\Rightarrow$ Area of rhombus $PQRS=\frac{PR\times QS}{2}$

$\Rightarrow$ $\frac{10\times 6.6}{2}$

$\therefore$ Area of rhombus $PQRS=33c{m}^2$