Question

The side of a square is 10 cm. Find the area of the circumscribed circle. [π = 3.14]

Answer 1

If a circle is circumscribed in a square, then the diagonal of the square is equal to the diameter of the circle.

Diagonal of the square of the suquare `= sqrt(2)xx"Side of the square"`

`= sqrt (2)xx10`

`= 10sqrt(2)  "cm" `

Diagonal = Diameter `= 10 sqrt(2)  "cm"`

∴ `r = 5sqrt(2)  "cm"`

Now, 

Area of the circumscribed circle = πr² 

`= 3.14 × (5sqrt(2)) `

= 3.14 × 50

= 157 cm²