Question

A square is inscribed in a circle of radius 6 cm. Find the area of the square. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.

Answer 1

Let the radius of the circle = r = 6cm
Now,
diagonal of a square = diameter of a circle
= 2r
= 2 x 6
= 12cm
Also,
`sqrt(2)` x side of a square = diagonal of a square
⇒ `sqrt(2)` x side = 12

⇒ side = `(12)/sqrt(12)`
= `6sqrt(2)"cm"`
∴ Area of a square
= (Side)²
= `(6sqrt(2))^2`
= 72cm².