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DRQP is a small square of side a in the corner of a big square ABCD of side A. What is the ratio of the area of the quadrilateral PBRQ to that of the square ABCD, given A/a = 3?
  • a)
    2/9
  • b)
    1/6
  • c)
    1/3
  • d)
    2/7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
DRQP is a small square of side a in the corner of a big square ABCD of...
Area of triangle PAB = Area of triangle RCB (By symmetry)
∴ Area of Δ PAB = ½ × PA × AB
= ½ × 2A/3 × A = A2/3
Area of ΔRCB = A2/3
Now, Area of ABCD = Area of DRQP + Area of PAB + Area of RCB + Area of PBRQ
A2 = a2 + A2/3 + A2/3 + Area of PBRQ
As, A/a = 3 ⇒ a = A/3
 Area of PBRQ
⇒ Area of PBRQ = 
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DRQP is a small square of side a in the corner of a big square ABCD of side A. What is the ratio of the area of the quadrilateral PBRQ to that of the square ABCD, given A/a = 3?a)2/9b)1/6c)1/3d)2/7Correct answer is option 'A'. Can you explain this answer?
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