Question
Download Solution PDFIn the given figure, PQRS is a quadrilateral. If QR = 18 cm and PS = 9 cm, then what is the area (in cm2) of quadrilateral PQRS?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExtend the line QP and RS they will meet at T and they will form an equilateral triangle
∆QRT is an equilateral triangle with side = 18 cm,
⇒ Area of the ∆QRT = √3/4 × 18 × 18 = 81√3 cm2
⇒ ∆TSP is the right angle triangle with PS = 9 cm,
⇒ TS = 9 tan 30° = 9/√3 cm
⇒ Area of the ∆TSP = 1/2 × 9/√3 × 9 = (27√3)/2 cm2
Now Area of quadrilateral PQRS = Area of ∆QRT - Area of ∆TSP
⇒ Area of quadrilateral PQRS = [81√3 - (27√3)/2]
∴ Area of quadrilateral PQRS = (135√3)/2 cm2
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