Question

a round thali has 2 inbuit triangular sections serving vegetables and seperate semicircular area for keeping rice or chappati . if the radius of thali is 21 cm , find the area of the semicircle excluding the 2 triangular sections

Answer 1

The area of the semicircle excluding the 2 triangular sections is 252 cm².

Step-by-step explanation:

Referring to the figure attached below, we have

• A round thali with centre O and AOB as the diameter.

• It also has 2 inbuilt triangular sections in one semi-circular half for serving vegetables and another semi-circular area for serving rice or chapati.

The radius of the thali, r = 21 cm

Since we have to find the area of the semicircle excluding the 2 triangular sections i.e., the area of the shaded portion as shown in the figure attached below, which will be given as,

Area of the shaded portion = [Area of semicircle] – [Area of ∆ ABC]

Now,  

Area of semicircle = ½ * πr² = ½ * (22/7) * (21)² = 11 * 3 * 21 = 693 cm²

And,

Area of ∆ ABC = ½ * base * height = ½ * AB * OC = ½ * 42 * 21 = 21 * 21 = 441 cm²

Thus,  

The area of the semicircle excluding the 2 triangular sections is given by,

= Area of the shaded portion

= 693 – 441

= 252 cm²

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