A circle is inscribed in an equilateral triangle of side a .then the area of square inscribed in the circle is

Question

A circle is inscribed  in an equilateral triangle of side a .then the area of square inscribed in the circle is

Rohit · Accepted Answer

The the radius of the circle is given by the formula r=(3^(1/2)×a)/6.

Now the diameter of this circle would be the diagonal of the square.Which gives the side of the square as ((3/2)^(1/2)×a)/3

Therefor area of the square would be a^2.

It would be more helpful for you if you understood how the formula for radius of circle inscribed in an equilateral triangle.

Hope i was able to help.

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A circle is inscribed in an equilateral triangle of side a .then the area of square inscribed in the circle is

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Question : A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square are:
Option 1: $\sqrt3:4$
Option 2: $\sqrt3:8$
Option 3: $3\sqrt3:2$
Option 4: $3\sqrt3:1$

Question : A piece of wire 132 cm long is bent successively in the shapes of an equilateral triangle, a square, and a circle. The area will be largest in the shape of:
Option 1: Circle
Option 2: Equilateral triangle
Option 3: Square
Option 4: Equal in all the shapes