Question

Find the area and perimeter of the figure given above in which all corners are right angles and all measurements in centimetres

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Answer 1

$\color{green}\large\underline{\underline{To\:Find:}}$

$\mathtt{The\:Perimeter\:and\:Area\:of\:the\:figure}$

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$\color{blue}\large\underline{\underline{Concept:}}$

• $\textit{By finding the <strong>Area</strong> and <strong>Perimeter</strong> of the different rectangles}$

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$\color{purple}\large\underline{\underline{We\:Know:}}$

• $\mathtt{Perimeter\:of\:rectangle}$

$\mathrm{Perimeter =2(length + breadth)}$

• $\mathtt{Area\:of\:rectangle}$

$\mathrm{Area =length \times breadth}$

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$\color{lime}\large\underline{\underline{Solution:}}$

• $\underline{\mathtt{\rightarrow Perimeter}}$

$\textit{Perimeter of ANLM}$

$Length = 12 unit$

$Breadth = 2unit$

$Perimeter = 2(12 + 2) = 28 unit$

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$\textit{Perimeter of NBCD}$

$Length = 5 unit$

$Breadth = 2 unit$

$Perimeter = 2(5 + 2) = 14 unit$

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$\textit{Perimeter of IJKL}$

$Length = 5 unit$

$Breadth = 2 unit$

$Perimeter = 2(5 + 2) = 14 unit$

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$\textit{Perimeter of EFGH}$

$Length = 3 unit$

$Breadth = 2 unit$

$Perimeter = 2(3 + 2) = 10 unit$

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$\therefore Perimeter\:the\:figure = ANLM + NBCD + IJKL + EFGH$

$\Rightarrow (28 + 14 + 14 + 10) units$

$\Rightarrow 66 units$

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• $\underline{\mathtt{\rightarrow Area}}$

$\textit{Area of ANLM}$

$Length = 12 unit$

$Breadth = 2unit$

$Area = 12 \times 2 = 24 unit^{2}$

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$\textit{Area of NBCD}$

$Length = 5 unit$

$Breadth = 2unit$

$Area = 5 \times 2 = 10 unit^{2}$

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$\textit{Area of IJKL}$

$Length = 5 unit$

$Breadth = 2unit$

$Area = 5 \times 2 = 10 unit^{2}$

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$\textit{Area of EFGH}$

$Length = 3 unit$

$Breadth = 2unit$

$Area = 3 \times 2 = 6 unit^{2}$

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$\therefore Area\:the\:figure = ANLM + NBCD + IJKL + EFGH$

$\Rightarrow (24 + 10 + 10 + 6) unit^{2}$

$\Rightarrow 50 unit^{2}$

Answer 2

Given,

AK = 12 cm

BD= FG= JK= 2cm

BD= NC, FG=EH, JK= IL

Therefore, CE+HI = (12-6) = 6cm

perimeter of the quadrilateral= Sum of the sides

There fore, Perimeter = 12+7+7+5+5+2+2+2+3+3+6

Answer: 54 cm