Question

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Please help me with this maths problem


Class 9 ch-9 area of parallelogram and triangles

Question in the attachment

Answer is
$114 {cm}^{2}$
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Answer 1

The quadrilateral ABCD is made up of two right triangles: ΔDBC and ΔDAB

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Find the missing length of BD using Pythagoras Theorem, a² + b² = c²:

DB² + BC² = CD²

DB² + 8² = 17²

DB² = 17² - 8²

DB² = 225

DB = √225

DB = 15 cm

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Find the area of ΔDBC:

Area = 1/2 x base x height

Area of ΔDBC = 1/2 x 8 x 15 = 60 cm²

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Find the missing length of AB using Pythagoras Theorem, a² + b² = c²:

AB² + AD² = BD²

AB² + 9² = 15²

AB² = 15² - 9²

AB² = 144

AB = √144

AB = 12 cm

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Find the area of ΔDAB:

Area = 1/2 x base x height

Area of ΔDAB = 1/2 x 12 x 9 = 54 cm²

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Find area of quadrilateral ABCD :

ABCD = ΔDBC + ΔDAB

ABCD = 60 + 54 = 114 cm²

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Answer: Area of quadrilateral ABCD = 114 cm²