Step-by-step explanation:
First , Split the given figure into two parts i.e rectangle and a semi - circle.
\underline{ \underline{ \text{Given}}}: [/tex]
In rectangle :
- Length ( L ) = 14 cm
- Width ( W ) = 9 cm
Finding the area of a rectangle :
[tex] \sf{Area \: of \: a \: rectangle = L \times W}[/tex]
⤷ [tex] \sf{14 \: cm \times 9 \: cm}[/tex]
⤷ [tex] \sf{126 \: {cm}}^{2} [/tex]
Area of a rectangle = 126 cm ²
Now , In circle :
- Diameter ( d ) = 14 cm { Since In rectangle , length of both sides are equal }
- Radius ( r ) = [tex] \sf{ \frac{14 \: cm}{2} = 7 \: cm}[/tex]
[tex] \sf{Area \: of \: a \:semi - circle = \frac{1}{2} \pi \: {r}}^{2} [/tex]
⟷[tex] \sf{ \frac{1}{2} \times 3.14 \times {7}^{2} }[/tex]
⟷[tex] \sf{ \frac{1}{2} \times 3.14 \times 49}[/tex]
⟷[tex] \sf{ \frac{1}{2} \times 153.86 \: {cm}^{2} }[/tex]
⟷[tex] \sf{76.93 \: {cm}}^{2} [/tex]
Area of a semi - circle = 76.93 cm²
Now , We have :
- Area of a rectangle ( A ) = 126 cm ²
- Area of a semi - circle ( a ) = 76.93 cm ²
[tex] \sf{Area \: of \: a \: shaded \: part = A - a}[/tex]
⟷[tex] \sf{126 \: {cm}^{2} - 76.93\: {cm}}^{2} [/tex]
⟷[tex] \boxed{ \sf{49.07 \: {cm}^{2} }}[/tex]
[tex] \red{ \boxed{ \boxed{ \underline{ \sf{Our \: final \: answer : 49.07 \: {cm}^{2} }}}}}[/tex]
Hope I helped ! ♡
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