Question

If the perimeter of the circle is 14π c.m., find the area of the square inside the circle​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, Perimeter of the circle is 14π cm

Let assume that radius of circle = r cm.

Now, as it is given that

$\rm \: Perimeter_{(circle)} = 14 \: \pi$

$\rm \: 2\pi \: r = 14 \: \pi$

$\rm\implies \:r \: = \: 7 \: cm$

So,

$\rm\implies \:Diameter = 2r = 14 \: cm$

Let assume that ABCD be a square inscribed inside the circle.

As square ABCD is inscribed inside the circle.

So, Diagonal of a square ABCD is equals to diameter of circle.

$\rm\implies \:Diagonal \: of \: square = 14 \: cm$

We know,

$\boxed{ \rm{ \:Area_{(square)} \: = \: \frac{1}{2} {(Diagonal)}^{2} \: \: }}$

So, on substituting the value, we get

$\rm \: Area_{(square)} \: = \: \dfrac{1}{2} \times {14}^{2}$

$\rm \: Area_{(square)} \: = \: \dfrac{1}{2} \times 196$

$\rm\implies \:Area_{(square)} = 98 \: {cm}^{2}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Given,

Perimeter of a circle = 14π

To find,

the area of the square inside the circle

Solution,

Let radius = r

perimeter = 14π

2πr = 14π

2r = 14

r = 7cm

Diameter = 2r

= 14cm

Let us assume that ABCD is a square inside the circle

Diagonal of a square inscribed in a circle = diameter of a circle = 14cm

Area of a square = 1/2 (diagonal)^2

= 1/2 x 14 x 14

= 98cm^2

So, area of the square is 98cm^2