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Question

In the given pentagon, ratio of area of trapezium ABCD to area of BEC is 5:2 and AG = 6 cm, EF = 4 cm. Find the length of BC if AD = 6 cm.


  1. 6 cm
  2. 8 cm
  3. 9 cm
  4. 10 cm


Solution

The correct option is C 9 cm
Area of trapezium ABCD
    = 12×(Sum of parallel sides)×height
    = 12×(AD+BC)×AG
    = 12×(6+BC)×6
    = 3×(6+BC)

Area of BEC =  12×base×height
                        =  12×BC×EF
                        =  12×BC×4
                        = BC×2

According to given condition,
area of ABCDarea of BEC=523×(6+BC)BC×2=526+BCBC=533×(6+BC)=5×BC18+3(BC)=5(BC)18=2(BC)BC=182=9 cm

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