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In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of...

Mathematics
WAEC 2001

In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ∆LMN is 18cm2, find the area of the quadrilateral MPQN

  • A. 3cm2
  • B. 6cm2
  • C. 14cm2
  • D. 24cm2
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Correct Answer: Option C
Explanation

\(\frac{LM}{LP} = \frac{3}{4}\)

\(\frac{Area of LMN}{Area of LPQ} = \frac{3^2}{4^2}\)

Area of LPQ = \(\frac{16}{9}\times 18 = 32 cm^2\)

Area of quadrilateral MPQN = 32 – 18 = \(14 cm^2\)


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