Question

if the area of a semicircle be 77sq.cm find its perimeter​

Answer 1

Answer:

Answer. Therefore,perimeter is 36cm

Answer 2

$\large{\underline{\underline{\sf{ \maltese \: {Given:-}}}}}$

• Area of the semicircle = 77 cm²

$\large{\underline{\underline{\sf{ \maltese \: {To \: find:-}}}}}$

• Perimeter of the circle = ?

• The perimeter = ?

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

➊ We know that:–

$\qquad \bull \: \bf{Area \: of \: circle =Area ~of~semicircle \times 2}$

$\qquad \quad {:} \longrightarrow \sf{Area \: of \: circle = \bigg(77 \times 2 \bigg) {cm}^{2} }$

$\qquad \quad {:} \longrightarrow \sf{Area \: of \: circle =154 \: {cm}^{2} }$

• Let us first find the radius of the circle:–

➋ We know that :–

$\qquad \bull \: \bf{Area \: of \: circle =\pi \: \bigg \{ {r}^{2} \bigg \} }$

$\qquad \quad {:} \longrightarrow \sf{ 154 = \dfrac{22}{7} \times {r}^{2} }$

$\qquad \quad {:} \longrightarrow \sf{ \cancel{154}^{\large7} \times \frac{7}{ \cancel{22}_{\large{1}}}= {r}^{2} }$

$\qquad \quad {:} \longrightarrow \sf{ 7 \times 7 = {r}^{2} }$

$\qquad \quad {:} \longrightarrow \sf{ 49 = {r}^{2} }$

$\qquad \quad {:} \longrightarrow \sf{ {r}^{2} = 49 }$

$\qquad \quad {:} \longrightarrow \sf{ {r} = \sqrt{ 49} }$

$\qquad \quad {:} \longrightarrow \sf{ \underline{ \boxed {\sf{{r} =7 }}}}$

$\quad \therefore \: \bf{radius = 7 \: cm }$

Now perimeter:–

$\qquad \quad {:} \longrightarrow \sf{ perimeter = 2 \times \dfrac{22}{7} \times 7 }$

$\qquad \quad {:} \longrightarrow \sf{ perimeter = 2 \times \dfrac{22}{ \cancel{7} _{ \large{1}} } \times \cancel 7 ^{ \large{1}} }$

$\qquad \quad {:} \longrightarrow \sf{ perimeter = 2 \times 22 }$

$\qquad \quad {:} \longrightarrow \sf{ perimeter = 44 }$

$\quad \therefore \: \bf{perimeter = \underline {\underline{44 \: cm} }}$

$\large{\underline{\underline{\sf{ \maltese \: {Answer:-}}}}}$

• The perimeter of the circle is 44 cm