Question

the shape of garden is a rectungular in the middle and the Semi circle at the ends. find the area and the perimeter of the garden.
LENGTH=30m
BREATH=5m​

Answer 1

$\huge \fbox{Answer}$

$\large \underline{ \underline {\frak{ \color{red}Given:}}}$

$\mapsto \sf{Length \: of \: rectangle=30m}$

$\mapsto \sf{Breadth \: of \: rectangle=5m}$

$\large \underline{ \underline {\frak{ \color{To}To \: find:}}}$

$\leadsto \sf{Perimeter \: and \:Area \: of \: garden. }$

$\large \underline{ \underline {\frak{ \color{blue}Formula \: required:}}}$

$\mp{ \boxed{ \rm{Perimeter_{(garden)}=Perimeter_{(rectangle)}+Perimeter _{(semi-circle)}}}} \mp$

$\mp { \boxed{ \rm{Area_{(garden)}=Area_{(rectangle)}+Area_{(semi-circle)}}}} \mp$

$\large \underline{ \underline {\frak{ \color{indigo}Concept \: used:}}}$

${ \rightarrow \sf{Radius \: of \: semi-circle \: is \: half \: of \: breadth \: of \: rectangle.}}$

$\large \underline {\underline{\frak{ \pink{According \: to \: Question: }}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=Perimeter_{(rectangle)}+Perimeter _{(semi-circle)}}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2(length + breadth)+ \frac{2\pi r}{2} }}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2(length + breadth)+ \frac{ \cancel 2\pi r}{ \cancel 2} }}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2(length + breadth)+ {\pi r}}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2(30m + 5m)+ { \frac{22}{7} \times \frac{5}{2}m }}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2 \times 35m+ { \frac{22}{7} \times \frac{5}{2}m }}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=2 \times 35m+ { \frac{ {\cancel {22}}}{7} \times \frac{5}{ \cancel 2}m }}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=70m+ { \frac{ {11}}{7} \times 5m }}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}=70m+ { \frac{ {55}}{7} m}}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}={ \frac{ {490+55}}{7} m}}}}$

${ ::\implies{ \sf{Perimeter_{(garden)}={ \frac{ {545}}{7} m=77.85m}}}}$

$\bf{Hence,}$

$\: \: \: \: \: \: \: \: \: \: \: \: \star{ \boxed{ \rm{Perimeter_{(garden)}=77.85m}}}\star$

$\bf{Then,}$

${:: \implies{ \sf{Area_{(garden)}=Area_{(rectangle)}+Area_{(semi-circle)}}}}$

${:: \implies{ \sf{Area_{(garden)}=length \times breadth+ \frac{\pi {r}^{2} }{2} }}}$

${:: \implies{ \sf{Area_{(garden)}=30m×5m+ \frac{ \frac{22}{7} \times { \frac{25}{4}} {m}^{2} }{2} }}}$

${:: \implies{ \sf{Area_{(garden)}=150 {m }^{2} + \frac{ \frac{22}{7} \times { \frac{25}{4}} {m}^{2} }{2} }}}$

${:: \implies{ \sf{Area_{(garden)}=150{m}^{2} + \frac{ \frac{11}{7} \times { \frac{25}{2}} {m}^{2} }{2} }}}$

${:: \implies{ \sf{Area_{(garden)}=150 {m }^{2} + \frac{ \frac{275}{14} {m}^{2} }{2} }}}$

${:: \implies{ \sf{Area_{(garden)}=150 {m }^{2} + { \frac{275}{14}} \times{2}=189.28{m}^{2} }}}$

$\bf{Hence,}$

$\: \: \: \: \: \: \: \: \: \: \: \star{ \boxed{ \rm{Area_{(garden)}=189.28 {m}^{2}(approx) }}} \star$