Find the area of the given figure which have all the squares corners.

Mathematics

2 answers:

elena55 [62]3 years ago

8 0

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 :

$\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}$

➣ l = 12 m
➣ b = 4 m

$\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 4}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =48}}}\\\\\qquad{\star{\underline{\boxed{\sf{\pink{A_{(Rectangle)} =48 \: {m}^{2}}}}}}} \end{gathered}$

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 :

$\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}$

➠ l = 5 m
➠ b = 2 m

$\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 5\times 2}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =10}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{A_{(Rectangle)} =10 \: {m}^{2}}}}}}} \end{gathered}$

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 :

$\longrightarrow{\pmb{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}}$

→ $\rm{A_{(Big)}}$ = Area of big rectangle
→ $\rm{A_{(Small)}}$ = Area of small rectangle

$\begin{gathered} \qquad{\longrightarrow{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 48 + 10}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 58}}} \\ \\ \quad{\star{\underline{\boxed{\sf{\red{Total \: Area =58\: {m}^{2}}}}}}} \end{gathered}$