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A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of a square inscribed in the circle?

A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of a square inscribed in the circle? Correct Answer 96

Side of triangle (a) = 24 cm

In-radius of triangle = a/2√3 = 24/2√3 = 4√3

As we know,

Diagonal of inscribed square = 2r = 2 × 4√3 = 8√3

Area of square = (Diagonal)2/2 = (8√3)2/2 = (64 × 3)/2 = 96 

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