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JAMB Mathematics 1979 Question 31

Question 31

Mensuration of Plane Shapes

(Numbers indicate the lengths of the sides of the triangles). If the area of Δ PQR is k2 sq. units, what is the area of the shaded portion?

Diagram for this question
  1. A.5/9 k2sq.units
  2. B.1/3 k2sq.units
  3. C.8/9 k2sq. units
  4. D.7/9 k2sq. units
  5. E.2/3 k2sq. units.
Show the answer and explanation

Answer: A (5/9 k2sq.units)

Explanation

The inner triangle is similar to the outer one with scale factor 2/3 (sides 2, 3⅓, 4 against 3, 5, 6), so its area is (2/3)² = 4/9 of k². The shaded part is k² − 4/9 k² = 5/9 k².