Question

A playground is in the form of a rectangle having semicircles on the shorter sides . Find its area if the length of the rectangular portion is 80 m and breadth is 42 m.​

Answer 1

Answer:

Let the length and breadth of the rectangular portion of the playground be I and b respectively.

Then, I = 80 m and b = 42 m.

Let r be the radius of each of the semicircular parts.

Then r = $\sf \dfrac{b}{2} = \dfrac{42}{2} m = 21m$

Area of the playground = Area of the rectangle + Area of two semicircles

$\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \:(l + b) + \bigg(2 + \dfrac{ \pi {r}^{2} }{2}\bigg) = lb + \pi {r}^{2} \\ \\ \\ \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: \bigg(80 \times 42 + \dfrac{ {22} }{7} \times 21 \times 21\bigg) {m}^{2} \\ \\ \\ \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: \bigg(3360 + 1386 \bigg) {m}^{2} \\ \\ \\ \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{ \displaystyle \sf \: 4746 {m}^{2} }} \\ \\ \end{gathered}\end{gathered}$

Hence , Area of play ground is 4746 m² .

Answer 2

Step-by-step explanation:

Answer:

Let the length and breadth of the rectangular portion of the playground be I and b respectively.

Then, I = 80 m and b = 42 m.

Let r be the radius of each of the semicircular parts.

Then r = \sf \dfrac{b}{2} = \dfrac{42}{2} m = 21m

2

b

=

2

42

m=21m

Area of the playground = Area of the rectangle + Area of two semicircles

\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \:(l + b) + \bigg(2 + \dfrac{ \pi {r}^{2} }{2}\bigg) = lb + \pi {r}^{2} \\ \\ \\ \end{gathered} \end{gathered}\end{gathered}

:⟹(l+b)+(2+

2

πr

2

)=lb+πr

2

\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: \bigg(80 \times 42 + \dfrac{ {22} }{7} \times 21 \times 21\bigg) {m}^{2} \\ \\ \\ \end{gathered} \end{gathered} \end{gathered}

:⟹(80×42+

7

22

×21×21)m

2

\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: \bigg(3360 + 1386 \bigg) {m}^{2} \\ \\ \\ \end{gathered} \end{gathered} \end{gathered}

:⟹(3360+1386)m

2

\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{ \displaystyle \sf \: 4746 {m}^{2} }} \\ \\ \end{gathered}\end{gathered} \end{gathered}

:⟹

4746m

2

Hence , Area of play ground is 4746 m² .