Find the area of quadrilateral whose one diagonal is 20 cm long and the perpendiculars to this diagonal from other vertices are of length 9 cm and 15 cm.
Mensuration
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Question

Find the area of quadrilateral whose one diagonal is 20 cm long and the perpendiculars to this diagonal from other vertices are of length 9 cm and 15 cm.

KnowledgeBoat · Accepted Answer

Consider ABCD as a quadrilateral in which BD = 20 cm, AY = 15 cm and CX = 9 cm. Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD Area of triangle = × base × height ∴ Area of quadrilateral ABCD = × BD × AY + × BD × CX Substituting the values we get, Area of quadrilateral ABCD = x BD x (AY + CX) = x 20 x (15 + 9) = 10 x 24 = 240 cm² Hence, area of quadrilateral = 240 cm².

Mathematics

Find the area of quadrilateral whose one diagonal is 20 cm long and the perpendiculars to this diagonal from other vertices are of length 9 cm and 15 cm.

Mensuration

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