Question

In the given figure PQRS is a rectangle inscribed in the circle. If PS = 5 cm and PQ = 12 cm, find the area of un-shaded region. (Use π =22/7)​

Answer 1

Answer:

392.5cm^.

Step-by-step explanation:

area of circle =( 22/7×12×12 )cm^.

=452.4cm^

area of rectangle =l×b

=12cm×5cm= 60cm^.

Unshaded region = 452.5cm^-60cm

=392.5cm^.

Answer 2

★ Question Given :

• In the given figure PQRS is a rectangle inscribed in the circle. If PS = 5 cm and PQ = 12 cm, find the area of un-shaded region. (Use π =22/7)

★ Required Solution :

✩ Values Given to us :

• ⟾ PS = 5 cm

• ⟾ PQ = 12 cm

• ⟾ (Use π =22/7)

✩ Construction Needed :

• ⟾ Draw a Diagonal in given figure in rectangle PQRS. As shown in Figure Attached Above !

★ In ∆ PQS

✩ By Pythagoras Theorum :

• ⟾ H² = P² + B²

• ⟾ SQ² = PQ² + PS²

• ⟾ SQ² = (12)² + (5)² cm

• ⟾ SQ² = 144 + 25 cm

• ⟾ SQ² = 169 cm

• ⟾ SQ² = √ 169 cm

• ⟾ SQ² = 13 cm [ Hypotenuse ]

✩ Diagonal = Diameter

• ⟾ Radius of Circle = 13 / 2

✩ Area of Circle = π r² :

• ⟾ Area = 22/ 7 × (13/ 2)²

• ⟾ Area = 132.66 cm²

✩ Area of Rectangle PQRS :

• ⟾ Area = l × B

• ⟾ Area = 12 × 5 cm

• ⟾ Area = 60 cm²

✩ Area of Unshaded Region :

• ⟾ Area of Circle - Area of Rectangle

• ⟾ Area of Unshaded region = 132.66 - 60 cm²

• ⟾ Area of Unshaded region = 72.66 cm²

Area of Unshaded region = 72.66 cm²

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