Question

Find the area of the shaded region in figure,

If PR = 24cm, PQ =7cm and O is the centre of the circle

Answer 1

Answer:

Area of shaded region is 161.54 cm^2.

Step-by-step explanation:

On observing the diagram, we get :

Area of the shaded region = Area of semi circle - area of the right angled triangle.

We know, intersecting lines from the end points of diameter, intersects at 90°.

So,

Area of the ΔPQR = 1 / 2 x PR x PQ

Area of ΔPQR = 1 / 2 x 24 cm x 7 cm

Area of ΔPQR = 12 x 7 cm^2

Area of ΔPQR = 84 cm^2

Now,

As QR is the  diameter of the circle,

Radius of the circle = 25 / 2 cm

Then,

Area of semi circle = 1 / 2 x π r^2

Area of semi - circle = ( 22 x 25 x 25 ) / ( 2 x 7 x 2 x 2 )

Area of semi  - circle = 245.54 cm^2

Therefore,

Area of shaded region = 245.54 cm^2 - 84 cm^2

Area of shaded region = 161.54 cm^2

Answer 2

Answer:

161.5 cm²

Step-by-step explanation:

Given, PR = 24 cm, PQ = 7 cm.

From figure:

In ΔPQR By Pythagoras theorem, we get

⇒ PR² + PQ² = RQ²

⇒ 24² + 7² = RQ²

⇒ 576 + 49 = RQ²

⇒ 625 = RQ²

⇒ RQ = 25 cm.

∴ Area of the shaded region = Area of semicircle - Area of ΔPQR

                                                = (1/2)πR² - (1/2) * b * h

                                                = (1/2) * (22/7) * (25/2)² - (1/2) * 24 * 7

                                                =  13750/56 - 84

                                                = 245.5 - 84

                                               = 161.5 cm².

Hope it helps!