Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.
Mensuration
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Question

Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.

KnowledgeBoat · Accepted Answer

Quadrilateral ABCD is shown in the figure below: Area of Δ DAB = x base x height = x DA x AB = x 24 x 32 cm² = 12 x 32 cm² = 384 cm² By using the Pythagoras theorem, AD² \+ AB² = BD² ⇒ 24² + 32² = BD² ⇒ 576 + 1,024 = BD² ⇒ 1,600 = BD² ⇒ BD = ⇒ BD = 40 cm In triangle BCD, Let the sides of the triangle be: a = 40 cm, b = 52 cm and c = 52 cm. The semi-perimeter s: ∵ Area of Δ BCD = = cm² = cm² = cm² = 960 cm² Therefore, area of quadrilateral ABCD = Area of Δ DAB \+ Area of triangle BCD = 384 \+ 960 cm² = 1344 cm² Hence, the area of quadrilateral ABCD is 1344 cm².

Mathematics

Calculate the area of quadrilateral ABCD in which AB = 32 cm, AD = 24 cm, ∠A = 90° and BC = CD = 52 cm.

Mensuration

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