Question

I 4 m
10. A rectangular lawn 80 m long and 50 m wide has
a gravel path 4 m wide running all around it. Find
the area of the path. [HINT: The length and breadth
increase by 4 m + 4 m.]
1.4 m
80 m
50 m.​

Answer 1

⠀⠀⠀⠀⠀⠀$\star{\underline{\bf{Required\: figure}}}$

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Given

• Length of the rectangular lawn is 80m.
• Width of the rectangular lawn is 50m.
• Width of path is 4m.

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To find

• Area of the path around the lawn.

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Solution

• Firstly, we will calculate area of ABCD.

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For ABCD

• Length = 80m + 4m + 4m
• Length = 89m

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• Width = 50m + 4m + 4m
• Width = 59m

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\large{\boxed{\boxed{\bf{Area_{(Rectangle)} = Length \times Breadth}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(ABCD)} = 89 \times 59}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(ABCD)} = 5,251\: m^2}$

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• Now,

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For PQRS

• Length = 80m
• Breadth = 50m

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(PQRS)} = 80 \times 50}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(PQRS)} = 4,000\: m^2}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Calculating\: the\: area\: of\: path}}}$

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$\boxed{\bf{\bigstar{Area_{(Path)} = Area_{(ABCD)} - Area_{(PQRS)}{\bigstar}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(Path)} = 5,251 - 4,000}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_{(Path)} = 1,251\: m^2}$

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Hence,

• The area of path is 1,251 m².