Question

the area of a circle whose radius is the diagonal of a square whose area is 4 is

Answer 1

area of square = 4 sq. units
⇒ a² =4
⇒side ,a = 2 units
now by Pythagoras theorem,
diagonal length = √((2)²+ (2)²
                         =2√2 units
so, radius of circle = 2√2 units
area of circle = π r²
                      =  π (2√2)²
                      =8π sq. units
so, area of circle = 8π sq. units.

Answer 2

Given : Area of a square = 4sq.un
Let `a` be the side of the square then a² = 4
∴a = √4 = 2
∴side of the square = 2 units
Let the diagonal of the square be `d`
With the diagonal and two adjacent sides of the square we get a right angled triangle
Here, d² = a² + a²  [By Pythagoras theorem]
⇒d² = 2²+2²
⇒d² = 4 + 4
⇒d = √8 = 2√2
∴diagonal = 2√2 units
Given that diagonal of the square = Radius of a circle
Radius = 2√2 units
Area of the circle = πr²
                            = π(2√2)²
                            =π ×8  
                            =22/7  × 8
                            = 176/7
                            = 25.1428 sq units
∴Area of the circle = 25.1428 sq units