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Question

Prove that a median divides a into two s of equal area.

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Solution

Given ΔABC
With AD as the median
BD=CD=12BC
To prove
area of ΔADB= area of ΔADC
Draw line ANBC
To find area, we use
Area of triangle =12 Base × Altitude
In ΔABD
BD is the base & AN is Altitude
area of ΔABD=12× Base × Altitude
=12×BD×AN
In ΔADC
area of ΔADC=12× Base × Altitude
=12×DC×AN
As BD=DC
Area of ΔADC=12×BD×AC
Ar(ΔABD)=Ar(ΔADC)


1040230_1076445_ans_1115ef5197a645e9a3e7ba485a134800.PNG

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