GATE | GATE CS 2018 | Question 5

What is the area of the circle which has the diagonal of the square as its diameter if the area of square is ‘ d ‘ ?

(A)

πd

(B)

πd²

(C)

(1/4) πd²

(D)

(1/2)πd

Answer: (D)

Explanation:

One important observation to solve 
the question :

Diagonal of Square = Diameter of Circle.

Let side of square be x. 

From Pythagoras theorem.
Diagonal = √(2*x*x)

We know area of square = x * x = d

Diameter = Diagonal =  √(2*d)

Radius = √(d/2)

Area of circle = π * √(d/2) * √(d/2) = 1/2 * π * d

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