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JAMB Mathematics 1980 Question 11

Question 11

Triangles and Quadrilaterals

In the figure below, PQ∥SR, ST∥RQ, PS = 7cm, PT = 7cm, SR = 4cm. Find the ratio of the area of QRST to the area of PQRS.

Diagram for this question
  1. A.56:77
  2. B.56:105
  3. C.28:105
  4. D.28:49
  5. E.56:49
Show the answer and explanation

Answer: B (56:105)

Explanation

QRST is a parallelogram with base 4cm and height 7cm: area 28cm². PQ = 7 + 4 = 11cm, so trapezium PQRS = ½(11 + 4) × 7 = 52.5cm². 28 : 52.5 = 56 : 105.