Question

Anyone please solve this step by step.

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Answer 1

Given:-

• ∠ABC = 90°
• AC = 41 c.m.
• BC = 40 c.m.
• AD = 16 c.m.

To Find: ar(ABCD) [Trapezium]

{Perpendicular height first}

In △ABC,

AC² = AB² + BC²

∴ AB² = AC² - BC²

⟹ AB² = (41)² - (40)²

⟹ AB² = (41 + 40)(41 - 40)

[Using Identity : a² - b² = (a + b)(a - b)]

⟹ AB² = 81

⟹ AB = √81 = 9 c.m.

We know,

Area of trapezium = (½)(Sum of || sides)(Distance between them)

∴ ar(ABCD) = (½)(40 + 16)(9) c.m.²

⟹ ar(ABCD) = (½)(56)(9) c.m.²

⟹ ar(ABCD) = (28)(9) c.m.²

⟹ ar(ABCD) = 252 c.m.²

∴ Area of the trapezium was 252 cm².