Question

A square of side 7 cm enclosed a circle touching all its four sides.then the area enclosed between the square and the circle is​

Answer 1

Given :-

Side of a square = 7cm

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Required to find :-

• Area enclosed between the square and the circle

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Formulae used :

$\tt{ Area \; of \; a \; square = \; side \times side }$

$\tt{ Area \: of \: a \: circle = \pi {r}^{2} }$

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Solution :

Given that ;

Side of the square = 7 cm

Area of the square = ?

Using the formula ;

$\tt{ Area \; of \; a \; square = \; side \times side }$

we get ,

$\longrightarrow{\tt{Area = 7cm \times 7cm}}$

$\longrightarrow{\tt{ Area = 49 {cm}^{2}}}$

So,

$\orange{\rightarrow{\tt{ Area \; of \; a \; square = 49{cm}^{2}}}}$

Similarly,

It is also mentioned that ,

The square has an enclosed circle touching all it's four sides .

So, from the above statement we can conclude that ;

Diameter of the circle = side of the square

So,

Diameter of the circle = 7cm

Radius of the circle = ?

$\tt{ Radius = \dfrac{ Diameter }{2}}$

$\tt{ r = \dfrac{ 7 }{2}}$

$\tt{ r = 3.5 cm }$

So,

Radius of the circle = 3.5 cm

Now ,

Using the formula :-

$\tt{ Area \: of \: a \: circle = \pi { r}^{2} }$

=> Here π = 22/7

$\tt{\rightarrow{ Area = \dfrac{22}{7} \times{ 3.5}^{2}}}$

$\tt{\rightarrow{ Area = \dfrac{269.5}{7}}}$

$\tt{\rightarrow{ Area = 38.5 {cm}^{2}}}$

So,

$\tt{\orange{\longrightarrow{Area \: of \; the \; circle = 38.5 {cm}^{2}}}}$

Hence,

Area enclosed = Area of the square - Area of the circle

So,

$\tt{\blue{\Rightarrow{ Area \; enclosed = 49 {cm}^{2} - 38.5 {cm}^{2}}}}$

$\tt{\red{\Rightarrow{ Area \; enclosed = 10.5{cm}^{2}}}}$

$\tt{\implies{\boxed{\green{\therefore{Area \; enclosed = 10.5{cm}^{2}}}}}}$

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Answer 2

Given :

A square of side 7 cm enclosed a circle touching all its four sides.

Side of the square = 7cm.

To be found :

The area enclosed between the square and the circle.

→Follow the attached image

Now,

To find area enclosed between the square and the circle, we have to find- area of circle and area of square.

Then, we have to subtract area of circle from the area of square.

So,

Area of square = (side)×(side) = (side)² unit sq.

Area of square = (7)² = 49 cm²

As from the given statement of question, we can get the diameter of the circle.

The diameter of the circle = side of the square

So, diameter = 7cm

Radius(r) of the circle = (7/2) cm

∴ 2r = diameter or diameter = (r/2)

Now,

Area of circle = πr² unit sq.

$\tt Area \: of \:the\: circle = \frac{ {\cancel{22}}^{11} }{\cancel{7} }\times\frac{\cancel{7}}{\cancel{2}} \times \frac{7}{2} \\ \\ \tt Area\: of\:the\:circle = \frac{77}{2} = 38.5 \:cm^{2}$

Now,

area enclosed between the square and the circle

= Area of square - Area of circle

= 49 - 38.5

= 10.5 cm²

Hence,

The area enclosed between the square and the circle is $\red{\underline{\underline{\tt{10.5 cm^{2} }}} }$.