Question

find the area of shaded region in the figure if PQ is equal to 12 p r is equal to 12 cm and o is the centre of the circle is equal to 3.14​

Answer 1

Answer:

1.68cm

Step-by-step explanation:

ANSWER

Radius OP=OQ=r=12 CM

=3.14×(12)

=(37.68−36)cm

=1.68 cm

Answer 2

We know, a semi-circle subtends an angle of 90°.

Since QR = Diameter, arc QR becomes a semi circle.

∴△PQR is a right angled triangle at P.

Or, by Pythagoras theorem,

QR² = PQ² + PR²

⟹ QR² = (12)² + (16)²

⟹ QR² = 144 + 256

⟹ QR² = 400 = (20)²

⟹ QR = 20 cm (diameter)

NOW, finding area of the semi-circle and triangle:-

Semi-circle:- (Find radius by "r = ½d")

½(πr²) = ½(3.14 × 10 × 10) cm² = 1.57 × 10² cm² = 157 cm²

Triangle:-

½bh = ½(12)(16) cm² = 8(12) cm² = 96 cm²

We observed,

Shaded region = Area of the semi circle - Area of the triangle

⟹ Shaded area = 157 cm² - 96 cm² = 61 cm².

@Psyclone