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Question

In this figure, triangle ABC is right - angled at B. Given that AB = 9 cm, AC = 15 cm and D and E are the mid-points of the sides AB and AC respectively, calculate the area of ΔADE.

A
13 cm2
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B
12 cm2
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C
13.5 cm2
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D
14 cm2
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Solution

The correct option is C 13.5 cm2
By pythogoras theorem, AB2+BC2=AC2
BC2=AC2AB2
BC2=15292
BC2=22581=144
BC=12 cm
As D and E are mid-points of AB and AC, by mid-point theorem, DEBC and DE=12BC=6 cm
Since, DEBC, we have ΔADE congruent to ΔABC
Area (ΔADE)Area (ΔABC)=DE2BC2
Area (ΔADE)12×AB×BC=(6)2BC2
Area (ΔADE)12×9×12=36144
Area (ΔADE)=14×9×6
Area (ΔADE)=274=13.5 cm2

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