In the given figure, P Q R S is a square of diagonal 7 √2 mathrm~cm. With P as centre and P Q as radius, the arc Q S is drawn. Find the area of the shaded region (in mathrmcm2 ).

Question

In the given figure, P Q R S is a square of diagonal 7 √2 mathrm~cm. With P as centre and P Q as radius, the arc Q S is drawn. Find the area of the shaded region (in mathrmcm2 ). (A) (21/2) (B) 14 (C) 21 (D) 42

Tardigrade Admin · Accepted Answer

Diagonal of the square =7 √2 mathrm~cm ⇒ text Side =(7 √2/√2)=7 mathrm~cm (Area of the shaded region) = (Area of the square) - (Area of the sector PQS) =72-(90°/360°) × (22/7) ×(7)2=(21/2) cm 2

Q. In the given figure, $PQRS$ is a square of diagonal $72 cm$ . With $P$ as centre and $PQ$ as radius, the arc $QS$ is drawn. Find the area of the shaded region (in $cm^{2}$ ).

$\frac{21}{2}$

14

21

42

Diagonal of the square $= 72 cm$
$\Rightarrow Side = \frac{7 2}{2} = 7 cm$
(Area of the shaded region) = (Area of the square) - (Area of the sector PQS)
$= 7^{2} - \frac{9 0 ^{\circ}}{36 0 ^{\circ}} \times \frac{22}{7} \times (7)^{2} = \frac{21}{2} c m^{2}$

Q. In the given figure, PQRS is a square of diagonal 72​ cm. With P as centre and PQ as radius, the arc QS is drawn. Find the area of the shaded region (in cm2 ).

221​

14

21

42

Diagonal of the square =72​ cm ⇒ Side =2​72​​=7 cm (Area of the shaded region) = (Area of the square) - (Area of the sector PQS) =72−360∘90∘​×722​×(7)2=221​cm2

Q. In the given figure, $PQRS$ is a square of diagonal $72 cm$ . With $P$ as centre and $PQ$ as radius, the arc $QS$ is drawn. Find the area of the shaded region (in $cm^{2}$ ).

$\frac{21}{2}$

Diagonal of the square $= 72 cm$
$\Rightarrow Side = \frac{7 2}{2} = 7 cm$
(Area of the shaded region) = (Area of the square) - (Area of the sector PQS)
$= 7^{2} - \frac{9 0 ^{\circ}}{36 0 ^{\circ}} \times \frac{22}{7} \times (7)^{2} = \frac{21}{2} c m^{2}$