Question

Find the area of the shaded region in fig, If PQ = 24 cm, PR = 7 cm and O is the centre of the circle ​

Answer 1

Area of shaded region = Area of semicircle - Area of triangle

Clearly, radius of circle = 25/2

Area = πr²/2 - PQxPR

= (22/7 x (25/2)²)/2 - 1/2x24x7

= 161cm² approx

Hope this helps... Thank you..

Answer 2

Area Of Shaded Region = 161.3 cm²

Step-by-step explanation:

GIVEN

PQ = 24 cm

PR = 7 cm

O is the centre of the circle

___________________________

TO FIND

Area Of Shaded Region

___________________________

We know that,

Hypotenuse² = Base² + Height²

Here,

Base = PR = 7 cm

Height = PQ = 24 cm

Hypotenuse = QR = ?

Hypotenuse² = Base² + Height²

QR² = PR² + PQ²

QR² = 7² + 24²

QR² = 49 + 576

QR² = 625

QR = √625

QR = 25

QR = 25 cm

___________________________

Now,

OR is the radius of circle

We know that,

Diameter = 2 × Radius

Radius = Diameter / 2

Radius = 25 / 2

Radius = 12.5

Radius = 12.5 cm

___________________________

We know that,

Area Of Triangle = ½ × Base × Height

Here,

Base = PR = 7 cm

Height = PQ = 24 cm

Area Of Triangle = ½ × 7 × 24

Area Of Triangle = 0.5 × 7 × 24

Area Of Triangle = 84

Area Of Triangle = 84 cm²

___________________________

We know that,

Area Of Semicircle = ½ × π × r²

Area Of Semicircle = ½ × 3.14 × 12.5²

Area Of Semicircle = 0.5 × 3.14 × 156.25

Area Of Semicircle = 245.3

Area Of Semicircle = 245.3 cm²

___________________________

We know that,

Area Of Shaded Region = Area Of Semicircle - Area Of Triangle

Area Of Shaded Region = 245.3 - 84

Area Of Shaded Region = 161.3

Area Of Shaded Region = 161.3 cm²