Question

If the difference of areas of the circumcircle and the incircle of a square is 154 sq cm then what is the area of the square?​

Answer 1

Answer:

Let the height of the triangle be h units and three sides of the triangle be x cm.

⇒ h2 + (x/2)2 = x2

∴ h = √3x/2

⇒ Radius of the circumcircle = 2/3 × h = x/√3

⇒ Radius of incircle = 1/3 × h = x/2√3

⇒ π(x2/3 – x2/12) = 154

⇒ 22/7 × x2/4 = 154

⇒ x = 14

∴ Area of the equilateral triangle = √3/4 × 14 × 14 = 49√3 cm2