Question

5. In the figure, E is the midpoint of the median AD of
the AABC. If ar(AABE ) = 8cm2, then
find the area of the AABC.
8cma
B
D​

Answer 1

Answer:

Given, AD is the median of triangle ABC.

So, AD will divide triangle ABC into two triangles of equal area.

So, AD will divide triangle ABC into two triangles of equal area.Thus,

Area of triangle (ABD) = Area of triangle ( ADC )

or, Area ( △ABD ) = 1 / 2 Area (△ABC ) ..... (1)

Again, E is the mid-point of AD.

So, BE will be the median of triangle ABD.

So, Area of triangle ( ABE ) = Area of triangle ( BED )

or, Area (△ABE ) = 1 / 2 Area (△ABD )

Therefore, Area (△ABE ) = 1 / 4 Area (△ABC ) ..[ using ( 1 ) ]

Hence proved!!

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