Question

The area of the largest possible square inscribed in a circle of unit radius is

Answer 1

Answer:

The area of the largest possible square inscribed in a circle of unit radius is 2 sq units

Step-by-step explanation:

the largest possible square inscribed in a circle have Diagonal = Diameter of circle

Circle has unit radius

=> Diameter = 2 units

Diagonal = 2 unit

in a sqaure Diagonal = Side√2

=> Side√2=  2

=> Side = √2

Area of a square = side² = √2² = 2 sq units

The area of the largest possible square inscribed in a circle of unit radius is 2 sq units

Answer 2

Answer:

The area of the largest square inscribed in a circle of unit radius is 2 sq units.

Step-by-step explanation:

Given a circle of unit radius.

The largest square that can be inscribed in a circle have diagonal equal to the diameter of circle

Length of diagonal = diameter of circle

                                $=2\times 1 =2\ units$

Let the length of side of square be $x$

In a square, length of diagonal = $x\sqrt{2}$

                                         $\implies 2=x\sqrt{2}\implies x=\frac{2}{\sqrt{2} } =\sqrt{2} units$

Area of a square,  $A=x^{2}$

                                  $=\sqrt{2} ^{2} =2sq.\ units$

Therefore the area of the largest square inscribed in a circle of unit radius is 2 sq units.