Question

3. The radius of a semi-circle shaped plot is 21
meter. Find its area and perimeter.​

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

Area=(1/2).pi.r^2  

= (1/2)×22/7×21×21 sq.m

=11×3×21 sq.m.  

=693 sq.m. , Answer.

Perimeter =pi.r+2r

= r(pi +2)

=21(22/7+2)

=21×36/7

=3×36

=108 m. , Answer

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Answer 2

→ To Find :

• Area of the semi-circle .

• Perimeter of the Semi-circle .

→ Given :

Radius of the Semi-circle = 21 m

→ We Know :

Area of circle :

$\boxed{\mathtt{A_{c} = \pi r^{2}}}$

Perimeter of a Circe :

$\boxed{\mathtt{P_{c} = 2\pi r}}$

Where ,r Is the radius of the Circle .

→ Concept :

We Know that the Semi-circle is the exact half of a circle,so we get the relation as :

$\mathtt{Circle = 2 \times Semi-circle}$

Or

$\mathtt{Semi-circle = \dfrac{circle}{2}}$

Hence ,the Formulae formed for Semi-circle are :

Area of a Semi-circle :

We Know the area for Circle i.e.

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

So the using the relation :

$\mathtt{Semi-circle = \dfrac{circle}{2}}$

We Get :

$\mathtt{Semi-circle = \dfrac{\pi r^{2}}{2}}$

Hence ,the formula for area of a Semi-circle is $\mathtt{A_{s} = \dfrac{\pi r^{2}}{2}}$

Perimeter of a Semi-circle :

We Know the formula for Perimeter for Circle i.e.

Perimeter of circle = $2\pi r$

So the using the relation :

$\mathtt{Semi-circle = \dfrac{circle}{2}}$

We Get :

$\mathtt{Semi-circle = \dfrac{\cancel{2}\pi r + 2r}{\cancel{2}}}$

$\mathtt{Semi-circle = \pi r + 2r}$

$\mathtt{Semi-circle = (\pi + 2)r}$

Hence ,the formula for Perimeter of a circle is $\mathtt{P_{s} = (\pi + 2)r}$

→ Solution :

Area of the Semi-circle :(Taking π = 22/7)

Using the formula ,

$\mathtt{A_{s} = \dfrac{\pi r^{2}}{2}}$

and Putting the value of π and r in the formula ,we get :

$\mathtt{\Rightarrow A_{s} = \dfrac{\dfrac{22}{7} \times 21^{2}}{2}}$

$\mathtt{\Rightarrow A_{s} = \dfrac{\dfrac{22}{7} \times 441}{2}}$

$\mathtt{\Rightarrow A_{s} = \dfrac{\dfrac{22}{\cancel{7}} \times \cancel{441}}{2}}$

$\mathtt{\Rightarrow A_{s} = \dfrac{22 \times 63}{2}}$

$\mathtt{\Rightarrow A_{s} = \dfrac{\cancel{22} \times 63}{\cancel{2}}}$

$\mathtt{\Rightarrow A_{s} = 11 \times 63}$

$\mathtt{\Rightarrow A_{s} = 693m^{2}}$

Hence ,the area of the Semi-circle is 693 m².

Perimeter of the Semi-circle :(π = 22/7)

Using the formula ,

$\mathtt{P_{s} = (\pi + 2)r}$

and Putting the value of π and r in the formula ,we get :

$\mathtt{\Rightarrow P_{s} = \bigg(\dfrac{22}{7} + 2\bigg)21}$

$\mathtt{\Rightarrow P_{s} = \bigg(\dfrac{22 + 14}{7}\bigg)21}$

$\mathtt{\Rightarrow P_{s} = \bigg(\dfrac{36}{7}\bigg)21}$

$\mathtt{\Rightarrow P_{s} = \bigg(\dfrac{36}{\cancel{7}}\bigg)\cancel{21}}$

$\mathtt{\Rightarrow P_{s} = 36 \times 3}$

$\mathtt{\Rightarrow P_{s} = 108 m}$

Hence ,the Perimeter of the Semi-circle is 108 m.

→ Additional information :

• Perimeter of the rectangle = 2(lenth + breadth)

• Area of the rectangle = Length × Breadth

• Perimeter of the square = 4 × side

• Area of the square = (side)²