Question
Download Solution PDFIn the figure given below ABCD is a parallelogram, DP and DQ are perpendicular on sides AB and BC respectively, DP = 8 cm and DQ = 12 cm. If DP divides AB in the ratio 1: 2 and DQ divides BC in the ratio 1: 1 and area of ABCD is 72 cm2, then what is the area of quadrilateral PBQD?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFArea of parallelogram ABCD = 72 = AB × DP
AB = 72/8
AB = 9 cm
72 = BC × DQ
BC = 72/12
BC = 6 cm
AP = 9 × (1/3)
AP = 3 cm
CQ = 6 × (1/2)
CQ = 3 cm
Area of ∆APD = (1/2) × 3 × 8 = 12 cm2
Area of ∆CQD = (1/2) × 3 × 12 = 18 cm2
Area of quadrilateral PBQD = Area of parallelogram – Area of ∆APD – Area of ∆CQD
= 72 – 12 – 18 = 42 cm2Last updated on Jun 13, 2025
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