Question

In the following figure, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area  of the shaded region.

 

Answer 1

We have to find the area of the shaded portion. We have, `OE=20cm`and OEFG is a square.

Use Pythagoras theorem to find OF as,

`OF=(sqrt((20)^2+(20)^2))cm`

`= 20sqrt2 cm`

So, radius of the circle,

`OF=20sqrt2 cm`

Therefore area of the shaded region,

`"Area of the shade region=(Area of quadrant of circle)-(Area of square)"`

So,

Area of the shaded region =`(pi(OF)^2)/4-(OE)^2` 

`(22/7)((20sqrt2^2)/4)-(20)^2`

=`628-400`

`=228 cm^2`