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

We have been given the radius of the thali as 21 𝑐𝑚 . We can find the area of the shaded region as follows: 

By the diagram, we can infer that,

 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑟𝑒𝑔𝑖𝑜𝑛 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑒𝑚𝑖𝑐𝑖𝑟𝑐𝑙𝑒 − 𝐴𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐵𝐶

Area of semicircle= ${\mathrm{\pi r}}^2$ , where r is the radius of the semicircle.

$\begin{array}{r}\Rightarrow \text{ Area of semicircle }=\frac{22}{7}\times \frac{1}{2}\times {21}^2\\ \Rightarrow \text{ Area of semicircle }=693{\mathrm{cm}}^2\\ \text{ Now, Area of triangle }=\frac{1}{2}\times \text{ base }\times \text{ height }\end{array}$

Here, the base will be the diameter (2 × 21 𝑐𝑚) and the height will be the radius.

$\begin{array}{r}=\frac{1}{2}\times 42\mathrm{cm}\times 21\mathrm{cm}\\ =441{\mathrm{cm}}^2\end{array}$

⇒ 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑟𝑒𝑔𝑖𝑜𝑛 = (693 − 441) 𝑠𝑞. 𝑐𝑚 

Hence, 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑟𝑒𝑔𝑖𝑜𝑛 is equal to 252 𝑠𝑞. 𝑐𝑚