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

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

KnowledgeBoat · Accepted Answer

Given, AB = 24 cm AD = 32 cm ∠BAD = 90° BC = 52 cm CD = 52 cm Diagonal BD divides the quadrilateral into two triangles: △ABD and △BCD Area of right angle △ABD = × Base × Height = × AB × AD = × 24 × 32 = 12 × 32 = 384 cm2. Since ∠BAD = 90 , by applying pythagoras theorem ⇒ BD2 = BA2 + AD2 ⇒ BD2 = 242 + 322 ⇒ BD2 = 576 + 1024 ⇒ BD2 = 1600 ⇒ BD = ⇒ BD = 40 cm. Area of △BCD, Let BC = a = 52 cm, CD = b = 52 cm, BD = c = 40 cm By formula, Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD = 384 + 960 = 1344 cm2. Hence, area of quadrilateral ABCD = 1344 cm2.

Mathematics

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

Mensuration

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