Question

'E' is the mid point of median AD of triangle ABC. Show that, area of triangle ABE = 1/4 area of triangle ABC.​

Answer 1

Answer:

ar.(tri.BED)=1/4ar.(tri.ABC)

Step-by-step explanation:

given- D is the midpoint of BC and AD is the median of tri.ABC. E is the midpoint of AD. so,BE is the median of triangle BAD.

then,

proof-

area of triangle ABD = area of triangle ACD

area of triangle ABD = 1/2 of area of triangle ABC

now,

area of triangle BED = area of triangle BEA

area of triangle BED = 1/2 (area of triangle ABD)

{as BEA = 1/2 of ABD}

area of triangle BED = 1/2[1/2(area of triangle ABC)]

{as ABD = 1/2 of ABC}

area of triangle BED = 1/4 (area of triangle ABC)

hence,proved.

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