Question

Find the area of the shaded region , in which dimensions are given in centimeters.

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Answer 1

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Answer 2

✰ Solution :

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☞︎︎︎ Given :

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• AC = 15cm

• AB = 8cm

• ∠A = 90°

• Hight of BC = 4cm

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➪ ABC is a right angled triangle

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★ Finding BC

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• Pythagoras Theorem :

✞︎ H² = P² + B²

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☞︎︎︎ Where,

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• P = 15cm

• B = 8cm

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➪ H² = 15² + 8²

➪ H² = 225 + 64

➪ H² = 289

$➪ \large \rm \: \: {h}^{} = \sqrt{289}$

∴ H = 17cm

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• Now, Finding area of ABC

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$☞︎︎︎ \large \: \rm \: area \: = \dfrac{base \times height}{2}$

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$\large \implies \rm \: area = \dfrac{8 \times 15}{2} \\ \\ \\ \implies \rm \: \: \large \: area = \dfrac{ \cancel8 \: \: 4\times 15}{ \cancel2}$

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$\boxed{ \looparrowright \rm \large \: area = 60 {cm}^{2} }$

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• Now area of unshaded region

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$☞︎︎︎ \large \: \rm \: area \: = \dfrac{base \times height}{2}$

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• Base = 17cm

• Height = 4cm

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$\implies \large \rm \: area = \dfrac{17 \times 4}{2} \\ \\ \\ \implies \large \rm \: area = \dfrac{17 \times \cancel 4 \: \: 2}{ \cancel2}$

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$\boxed{ \looparrowright \rm \large \: area = 34 {cm}^{2} }$

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☞︎︎︎ Area of shaded region :

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= Area of ABC - Area of unshaded triangle

➪ 60cm² - 34cm²

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∴ Area of shaded region = 26cm²