Question

ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Prove that : ar(triangle BED) = 1/4ar( triangle ABC)

Answer fast Please.

Answer 1

Answer:

Step-by-step explanation:

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal area.

∴ Area (ΔABD) = Area (ΔACD)

⇒Area (ΔABD ) = (½) area (Δ ABC) ------------(1)

In ΔABD, E is the mid-point of AD.

Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = (1/2)Area (ΔABD)

Area (ΔBED) = (½ ) x(1/2) Area (ΔABC)         [From (1)]

∴ Area (ΔBED) = (1/4)Area (ΔABC).

Answer 2

Given -- A ∆ABC.

D is the mid-point of BC
and E is the mid-point of AD.

To prove : ar (∆BED) = 1/4 ar (∆ABC)

Proof : Since AD is the median of ∆ABC,

Therefore, ar (∆ABD) = ar (∆ADC)

=> ar (∆ABD) = 1/2 ar (∆ABC) ---(1)

Since BE is the median of ABD,

Therefore, ar (∆BED) = ar (∆BAE)

=> ar (∆BED) = 1/2 ar (∆ABD)

= 1/2 × 1/2 ar (∆ABC) (using (1)

Hence, ar (BED) = 1/4 ar (∆ABC)