Question

find the area of the shaded portion of the given rectangle ​

Answer 1

$\sf\Large{\underline{\underline{Solution:-}}}$

• Area of whole figure by using this formula:-

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{length \times breadth}\:}}\end{gathered}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{(5cm + 9cm) \times (6cm + 4cm)}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{14 \times 10}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{140cm^{2} }\:}}\end{gathered}$

∴The area of whole figure is 140cm².

⠀

Now find the area of all the triangles.

• Area of $\underline{\sf{\blue{Triangle \: I}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times b \times h\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 6cm \times 8cm\:}}\end{gathered}$

Area = $\sf{\cancel\dfrac{48}{2}}$ = 24cm².

∴ Area of triangle I is 24cm².

⠀

$\underline{\sf{\green{Now,}}}$

• Area of $\underline{\sf{\blue{Triangle \: II}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 5cm \times 4cm\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{20}{2}}}\end{gathered}$

Area = $\sf{\cancel\dfrac{20}{2}}$ = 10cm².

∴ Area of Triangle II

⠀

$\underline{\sf{\purple{Now,}}}$

• Area of $\underline{\sf{\blue{Triangle \: III}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 9cm \times 6cm\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{54}{2}\:}}\end{gathered}$

Area = $\sf{\cancel\dfrac{54}{2}}$ = 27cm².

∴The area of Triangle III is 27cm².

⠀

$\underline{\sf{\red{Now,}}}$

• find shaded portion.

Area of shaded portion = Area of whole figure – Area of all triangles.

$\Longrightarrow$Area of shaded portion = 140cm² – (24cm² + 10cm² + 27cm²)

$\Longrightarrow$Area of shaded portion = 140cm² – 61cm²

$\Longrightarrow$Area of shaded portion = 79cm²

∴ Area of shaded portion is 79cm²

Answer 2

$\sf\Large{\underline{\underline{Solution:-}}}$

• Area of whole figure by using this formula:-

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{length \times breadth}\:}}\end{gathered}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{(5cm + 9cm) \times (6cm + 4cm)}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{14 \times 10}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{140cm^{2} }\:}}\end{gathered}$

∴The area of whole figure is 140cm².

⠀

Now find the area of all the triangles.

Area of $\underline{\sf{\blue{Triangle \: I}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times b \times h\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 6cm \times 8cm\:}}\end{gathered}$

Area = $\sf{\cancel\dfrac{48}{2}}$ = 24cm².

∴ Area of triangle I is 24cm².

⠀

$\underline{\sf{\green{Now,}}}$

Area of $\underline{\sf{\blue{Triangle \: II}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 5cm \times 4cm\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{20}{2}}}\end{gathered}$

Area = $\sf{\cancel\dfrac{20}{2}}$ = 10cm².

∴ Area of Triangle II

⠀

$\underline{\sf{\purple{Now,}}}$

Area of $\underline{\sf{\blue{Triangle \: III}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{1}{2} \times 9cm \times 6cm\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{\dfrac{54}{2}\:}}\end{gathered}$

Area = $\sf{\cancel\dfrac{54}{2}}$ = 27cm².

∴The area of Triangle III is 27cm².

⠀

$\underline{\sf{\red{Now,}}}$

find shaded portion.

Area of shaded portion = Area of whole figure – Area of all triangles.

$\Longrightarrow$Area of shaded portion = 140cm² – (24cm² + 10cm² + 27cm²)

$\Longrightarrow$Area of shaded portion = 140cm² – 61cm²

$\Longrightarrow$Area of shaded portion = 79cm²

∴ Area of shaded portion is 79cm²

$\huge\colorbox{lime}{ᴍʀ.ᴀsʜɪᴛ࿐ ❤}$