Question

A round thali has 2 inbuilt triangular for serving vegetables and a separate semicircular area for keeping rice or chapati. If radius of the thali is 21 cm, find the area of the thali that is shaded in the figure.​

Answer 1

The area of the shaded region is 252 cm².

Step-by-step explanation:

Since, the thali is round so, it can be considered as a circle.

The radius of the circle = CO = 21 cm

The diameter of the circle = AB = 2 CO = (2*21)

                                                                 = 42 cm

The area of semi-circle AOBC =  πr²/2

                                                  = (22/7) × (21×21)/2

                                                  = 693 cm²

For triangle ABC,

CO is the height = 21 cm

AB is the base = 42 cm

∴ Area of triangle ABC = 1/2 (base × height)

                                     = 1/2(42×21)

                                    = 441 cm²

∴ Area of the shaded region = (Area of semi-circle AOBC - Area of triangle ABC)

= (693-441) cm²

= 252 cm²

Answer 2

Area of shaded part = 252 cm²

Step-by-step explanation:

Radius = 21 cm

OA = OC = OB = 21 cm

Area of the semi-circle = $\frac{1}{2} \pi r^2$

                                      $=\frac{1}{2} \times \frac{22}{7} \times21\times21$

Area of the semi-circle = 693 cm²

Area of triangle AOC = $\frac{1}{2}bh$

                                   $=\frac{1}{2}\times 21\times 21$

Area of triangle AOC = 220.5 cm²

Area of triangle BOC = Area of triangle AOC

Area of triangle BOC = 220.5 cm²

Area of shaded part = area of semi circle - area of AOC - area of BOC

                                 = 693 cm² - 220.5 cm² - 220.5 cm²

Area of shaded part = 252 cm²

To learn more...

1. Find the area of the shaded region if PAST is square of side 14cm and ALS and PLT are semicircle

https://brainly.in/question/7353537

2. Find the area of the shaded region in the adjoining figure, it being given that ABCD is a square of side 12 cm, CE= 4 cm, FA=5 cm,BG= 5 cm.

https://brainly.in/question/12579063