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Question

If the area of trapezium ABCE is 35 cm2, and CE = 8 cm, AE = 5 cm, find the area of BDC.

A
5 cm2
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B
6 cm2
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C
10 cm2
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D
12 cm2
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Solution

The correct option is A 5 cm2
Area of triangle
= Area of trapezium ABCE
- Area of rectangle ABDE

Area of trapezium ABCE
= 12×(Sum of parallel sides)×height
35 = 12×(AB+CE)×AE
35 = 12×(AB+8)×5
35×25 = AB+8 = 7×2 = 14
AB+8 = 14
AB = 14-8 = 6 cm

Area of rectangle ABDE
= length×breadth
= AB×AE = 6×5 = 30 cm2

Area of triangle = 35 - 30 = 5 cm2

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