Question

AD is the median of triangle ABC .Find the area of triangle ADC .If the area of triangle ABC is 52 cm2

Answer 1

ar(ABD) + ar (ADC) = ar( ABC ) 
ar(ADC) + ar (ADC) = ar(ABC) 
( since ar(ADC ) = ar(ABD) ) 
2 ar( ADC ) = ar (ABC ) 
ar ( ADC) = 1/2ar ( ABC ) 
ar(ADC) = 1/2 * 52 
ar(ADC) = 26 cm²

Answer 2

Given that the area of ∆ABC is 52cm² and AD is the median.


There is a theorem that :-


"Median of a triangle divides the triangle into two triangles of equal area"

Hence, the two triangles that are formed will be equal in area

=> ar(ADC) = ar(ADB)

and, ar(ADC) +ar(ADB) = ar(ABC)

=> ar(ADC) + ar(ADC) = ar(ABC)

(since, ar(ADB) = ar(ADC) )

=> 2ar(ADC) = ar(ABC)

=> ar(ADC) = ar(ABC)/2

=> ar(ADC) = 52/2

=> ar(ADC) = 26 cm²

Answer :- 26 cm²