Math, asked by bilalsiddique4369, 5 hours ago

Find the perimeter and area of the circle which touches each side of a square of length 4cm

Answers

Answered by diyavats1
0

Step-by-step explanation:

We draw a radius at an angle of 90 degrees from the first radii.

We observe that a square is formed.

This shows us that half a side of square =4 cm

Thus, length of one side= 4×2=8 cm

Perimeter = 4×side=4×8=32 cm

Answered by TwilightShine
16

Answer :-

  • The perimeter and area of the circle which touches each side of a square of length 4 cm are 25.14 cm and 50.28 cm² respectively.

To find :-

  • The perimeter and area of the circle which touches each side of a square of length 4 cm.

Step-by-step explanation :-

  • Here, it is given that a circle touches each side of a square and length of each side of the square is 4 cm.  

 

As the circle touches each side of the square (Side of the square = 4 cm), the radius will be equal to the side of the square.

_____________________

  • First let's find the perimeter (circumference) of the circle!  

We know that :-

 \underline{\boxed{\sf{Perimeter \: of \: a \: circle = 2 \pi r}}}

Here,

  • Radius = 4 cm.

  • pi = 22/7.

Therefore,

 \longrightarrow \: \tt{Perimeter = 2 \times \dfrac{22}{7} \times 4}

 \longrightarrow \: \tt{ Perimeter = \dfrac{44}{7} \times 4}

 \longrightarrow \: \tt{Perimeter = \dfrac{176}{7}}

 \longrightarrow \: \tt{Perimeter = 25.14\: cm}

_____________________

  • Now let's find the area of the circle!

We know that :-

 \underline{\boxed{\sf{Area \: of \: a \: circle = \pi {r}^{2}}}}

Here,

  • Radius = 4 cm.

  • pi = 22/7.

Therefore,

\longrightarrow \: \rm{Area =  \dfrac{22}{7} \times {4}^{2}}

 \longrightarrow \: \rm{Area =  \dfrac{22}{7} \times 16}

 \longrightarrow \: \rm{ Area = \dfrac{22}{7} \times 16}

 \longrightarrow \: \rm{ Area = \dfrac{352}{7}}

\longrightarrow \: \rm{Area = 50.28\: cm^2}

_____________________

Hence,

  • The perimeter of the circle = 25.14 cm.
  • The area of the circle = 50.28 cm².
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