Question
Download Soln PDFPerimeter of a quadrilateral ABCD is 120 cm. If BC = 48 cm, CD = 17 cm, AD = 40 cm and ∠A = ∠B = 90°, then area of quadrilateral ABCD (in cm2) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Soln PDF
Given:
BC = 48 cm, CD = 17 cm, AD = 40 cm
∠A = ∠B = 90°
Formula used:
Area of rectangle = Length × Breadth
Area of right-angled triangle = 1/2 × Base × Perpendicular
Hypotanesous2 = Base2 + Perpendicular2
Calculation:
In Δ DEC,
Perpendicular (DE) = √(DC2 - EC2)
⇒ DE = √(172 - 82)
⇒ DE = √(289 - 64)
⇒ DE = √225 = 15 cm
Now,
Area of Δ DEC
⇒ 1/2 × EC × DE
⇒ 1/2 × 8 × 15
⇒ 1/2 × 120 = 60 cm2
Now, AB = DE = 15 cm
Area of rectangle ABED
⇒ AB × AD
⇒ 15 × 40 = 600 cm2
Thus,
Area of quadrilateral ABCD
⇒ Area of Δ DEC + Area of rectangle ABED
⇒ 60 + 600
⇒ 660 cm2
∴ The correct answer is option (3).
Last updated on Apr 30, 2025
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