Answer:
The area of the given figure is 58 m².
Step-by-step explanation:
Dividing the given figure into two parts :
- ➛ Big rectangle
- ➛ Small rectangle
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Firstly, finding the area of bigger rectangle by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]
[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 4}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =48}}}\\\\\qquad{\star{\underline{\boxed{\sf{\pink{A_{(Rectangle)} =48 \: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the area of bigger rectangle is 48 m².
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Secondly, finding the area of smaller rectangle by substituting the values in formula :
[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]
[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 5\times 2}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =10}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{A_{(Rectangle)} =10 \: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the area of smaller rectangle is 10 m².
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Now, finding the total area of given figure by substituting the values in the formula :
[tex]\longrightarrow{\pmb{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}}[/tex]
- → [tex]\rm{A_{(Big)}}[/tex] = Area of big rectangle
- → [tex]\rm{A_{(Small)}}[/tex] = Area of small rectangle
[tex] \begin{gathered} \qquad{\longrightarrow{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 48 + 10}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 58}}} \\ \\ \quad{\star{\underline{\boxed{\sf{\red{Total \: Area =58\: {m}^{2}}}}}}} \end{gathered}[/tex]
Hence, the total area of the given figure is 58 m².
[tex]\rule{300}{2.5}[/tex]
