Question

THE Circumference of a circle is 44 cm.The area of a square inscribed in i

Answer 1

here,
circumference = 44cm
$radius \: r = \frac{44}{2\pi} \\ r = \frac{44 \times 7}{2 \times 22} \\ r = 7 \: cm$
so, diameter = 14cm = diagonal of inscribed square.
so,
2 a² = 14²
or,
a = 14/√2 or
a = 7√2 cm

so area of square is, a² = 49 × 2
= 98 cm²


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Answer 2

The area of a square inscribed in the circle is 98 cm².

Complete question:

The circumference of a circle is 44 cm. The area of a square inscribed in it is :

Concept used:

• First of all, we will find the radius of a circle with the help of a circumference formula then we will find the diameter of the circle.
• As we know, the diameter of a circle is equal to the diagonal of the inscribed square.
• From the formula of the diagonal of a square, we will find the side of a square then we can find the area of a square.

Formula used:

• Circumference of a circle, C = 2πr
• Diameter of a circle = 2 × radius
• Diagonal of a square, d = a√2
• Area of square = side × side or a²

where 'r' is the radius, 'd' is the diagonal, and 'a' is the side of the square.

Given:

Circumference of a circle = 44cm

To find : Area of a square inscribed in it

Solution:

Step1: Find the radius

Circumference of a circle, C = 2πr

C = 44 cm

44 = 2πr

$44 = 2 \times \frac{22}{7} \times r\\\\\44 = \frac{44}{7} \times r\\\\\44 \times r = 44 \times 7\\\\\r = \frac{44 \times 7}{44}$

r = 7 cm

Radius = 7 cm

Step2: Find the diameter

Diameter of a circle = 2 × radius

Diameter of a circle = 2 × 7 cm

Diameter of a circle = 14 cm

Step3: Find the side of a square

Diameter of a circle = diagonal of inscribed square = 14cm

Diagonal of a square, d = a√2

14  = a√2

$a = \frac{14}{ \sqrt2}$

By rationalizing the denominator we get

$a = \frac{14 \times \sqrt2}{ \sqrt2 \times \sqrt2}\\\\\a = \frac{14 \sqrt2}{ 2}$

$a = \frac{14 \sqrt2}{ 2}$

a = 7√2 cm

side of a square ,a = 7√2 cm

Step4: Find the area of a square

Area of square, A = side × side or a²

A = 7√2 × 7√2

A = 49 × 2                             [√2 × √2 = 2]

A = 98 cm²

Area of square =  98 cm²

Hence, the area of a square inscribed in the circle is 98 cm².

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