Area of Triangle ABC is 800cm2 AD is a median, E is the mid point of AD - Maths - Areas of Parallelograms and Triangles

Question

Area of Triangle ABC is 800cm2 AD is a median, E is
the mid point of AD If F is the mid point of AB then find that area
of Triangle AEF

Utsav · Accepted Answer

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Given ABC is a triangle and D is the midpoint of BC Fand E are the
midpoints of AB and AD respectively

Mid point theorem states that the line joining the midpoints of two
sides of a triangle is parallel to third side and equals to half of
the length of third side
F and E are the midpoints of AB and AD respectively Hence
FE∥BD and FE=12BD

Now as we know that median divides the triangle into two triangles
of equal area∴area∆ABD = area∆ADC =12 area
∆ABCHence area∆ABD = 12×800 cm2=400 cm2Now in
∆AFE and ∆ABD,∠AFE =∠ABD (corresponding angles
as FE∥BD and AB is a transversal)∠AEF=∠ADB
(corresponding angles as FE∥BD and AD is a
transversal)∠FAE =∠BAD(common)Hence by AAA similarity
∆AFE~∆ABD∴area∆AFEarea∆ABD
=(FE)2(BD)2=(12BD)2(BD)2=14Hence area∆AFE = 14area ∆ABD
=14×400 cm2=100 cm2

Area of Triangle ABC is 800cm2 . AD is a median, E is the mid point of AD. If F is the mid point of AB then find that area of Triangle AEF.

Area of Triangle ABC is 800cm² . AD is a median, E is the mid point of AD. If F is the mid point of AB then find that area of Triangle AEF.