Maths-

General

Easy

Question

# Find the area of square inscribed in a circle of radius 8 cm.

## The correct answer is: ∴ Area of the given square is 128 cm2.

### i Area of a square = side2

ii. Diameter of a circle = 2 × Radius

iii. All angles in a square are equal to 90°

iv. Diagonal of a square divides it into 2 right angled triangles.

Step-by-step solution:-

Let the given question be represented by the adjacent diagram.

We can observe that-

Diameter BD of the given circle = Diagonal of the Given Square ABCD

Now, we are given that for the given circle-

Radius = 8 cm.

We know that-

Diameter = 2 ×Radius

∴ Diameter = 2 × 8

∴ Diameter = 16 cm

For Δ ABD,

∠ BAD = 90° ................................................... (All angles of a square = 90°)

Hence, Δ ABD is a right angled triangle.

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse^{2} = sum of the squares of the remaining 2 sides

∴ (BD)^{2} = AB^{2} + AD^{2}

∴ 162 = AB^{2} + AB^{2} .............................. (Sides of a square are equal)

∴ 256 = 2AB^{2}

∴ 256 / 2 = AB^{2}

∴ 128 = AB^{2}

i.e. AB = √128 ..................................... (Taking square root both the sides)

∴ AB = 8 √2 cm

∴ Side of the given square = AB = 8 √2 cm ................................ (Equation i)

Area of square = side2

∴ Area of square = AB2

∴ Area of square = (8 √2)2 .......................................... (From Equation i)

∴ Area of square = 64 × 2

∴ Area of square = 128 cm2

Final Answer:-

∴ Area of the given square is 128 cm2.

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