Question

Construct a parallelogram $PQRS$ such that $PQ=4cm,PR=4.5cm$ and $\angle PQR={45}^{\circ }$. Then the area of the parallelogram (in $c{m}^2$) is:

• A. $15.4$
• B. $18.2$
• C. $8.8$
• D. $17.9$

Answer 1

The correct option is D $17.9$

$\Rightarrow$ Draw a line segment PQ = 4cm.

$\Rightarrow$ Construct an angle of ${45}^{\circ }$ at point Q.

$\Rightarrow$ Cut off PR = 4.5cm

$\Rightarrow$ Take P as a center with radius equal to QR and draw an arc.

$\Rightarrow$ Take R as a center with radius 4cm, draw an arc meeting previous arc at point S.

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

$\Rightarrow$ Draw RT $\perp$ PS

$\Rightarrow$ Measure length PS and RT.

$\Rightarrow$ $l\left(PS\right)=b=6.3cm$ and $l\left(RT\right)=h=2.84cm$

$\Rightarrow$ Area of parallelogram $PQRS=b\times h=6.3\times 2.84$

$\therefore$ Area of parallelogram $PQRS=17.89c{m}^2\approx 17.9c{m}^2$