Calculate the area of quadrilateral ABCD in which △BCD is equilateral with each side equal to 26 cm, ∠BAD = 90° and AD = 24 cm.
Mensuration
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Question

Calculate the area of quadrilateral ABCD in which △BCD is equilateral with each side equal to 26 cm, ∠BAD = 90 and AD = 24 cm.

KnowledgeBoat · Accepted Answer

Given △BCD is equilateral. Each side = 26 cm ∠BAD = 90 AD = 24 cm Since ∠BAD = 90 By applying pythagoras theorem in triangle BAD, ⇒ AB2 + AD2 = BD2 ⇒ AB2 + 242 = 262 ⇒ AB2 + 576 = 676 ⇒ AB2 = 676 - 576 ⇒ AB2 = 100 ⇒ AB = ⇒ AB = 10 cm. ⇒ Area of right angle triangle ABD = × Base × Height = × AB × AD = × 10 × 24 = 5 × 24 = 120. ⇒ Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD = 120 + 292.71 = 412.71 cm2. Hence, area = 412.71 cm2.

Mathematics

Calculate the area of quadrilateral ABCD in which △BCD is equilateral with each side equal to 26 cm, ∠BAD = 90° and AD = 24 cm.

Mensuration

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