Question

The area of ΔABC = 32 cm2. AD is a median and E is the mid-point of AD. Find the area of ΔBED.

Answer 1

Hello Mate!

In ∆ABC, AD is a median hence,

ar(∆ADB) = ar(∆ADC) = ½ ar( ∆ ABC )

ar(∆ADB) = ½ × 32 cm²

ar(∆ADB) = 16 cm²

Now, in ∆ADB BE is median hence,

ar(∆BED) = ar(∆AEB) = ½ ar(∆ABD)

ar(∆BED) = ½ × 16 cm²

ar(∆BED) = 8 cm²

Hence ar(∆BED) = 8 cm².

Have great future ahead!

Answer 2

here is your answer OK


Since AD is a median of triangle ABC
.`.ar(triangle ADB)=ar(triangle ADC)
ar(triangle ADB)= 1/2 ar(triangle ABC) ----[1]

Now, since E is the mid pt. of AD
.'. BD is a median of triangle ADB
=> ar(triangle BEA) = ar(triangle BED)

ar(triangle BED) =1/2 ar(triangle ADB)
=> ar(triangle BED) = 1/2 1/2 ar(triangle ABC)
=>ar(triangle BED) = 1/4 32 cm2
.'. ar(triangle BED) = 8 cm2