Question

Find the area of the shaded portion. Which is shown in the diagram

Answer 1

Hint: We have a square given in the diagram, and we have to find the area of the shaded region, so if we subtract 4 areas of the sector of the circle from area of rectangle then we will get an area of the shaded portion, because we can see in the diagram at all four corners a sector of the circle is formed.

Complete step-by-step answer:
Area of square =${21^2} = 441$
Area of sector ABC=$\dfrac{\theta }{{360}}\pi {r^2}$
Radius=10.5cm and angle of square is 90.
So area = $\dfrac{{90}}{{360}} \times \pi \times {\left( {10.5} \right)^2} = 86.590$
Hence area of 4 sectors = $86.59 \times 4 = 346.36$
Area of shaded region = area of square – total area of sectors
=441-346.36
=94.64 $c{m^2}$

Note: Whenever we get this type of question the key concept of solving is we have to understand the diagram and knowledge of finding the area of the sector. Half of the question is just solved by understanding that we have to subtract how much area from the total area, and remember the formula of finding the area of the sector.