Question

D is the mid-point of AC. E is on BC such that BE = `1/3` BC. Area of ΔABC = 48 cm². Find the area of ΔADB and ΔBDE.

Answer 1

Given:

• D is the midpoint of AC.
• E is on BC such that BE = `1/3` BC.
• Area of ΔABC = 48 cm².

Median is a line from any one vertex of a triangle to the mid-point of the opposite side.

Since, D is the mid-point of AC.

Therefore, BD is the median of ΔABC.

Median of a triangle divides it into two triangles of equal areas.

∴ ar(ΔADB) = ar(ΔBDC)

= `1/2` × ar(ΔABC) 

= `1/2 xx 48`

= 24 cm²

Now, ΔBDE and ΔBDC lie on the same base BC and have a common vertex D.

So, heights are same.

`(ar(ΔBDE))/(ar(ΔBDC)) = (1/2 xx BE xx h)/(1/2 xx BC xx h)`

⇒ `(ar(ΔBDE))/24 = (BE)/(BC) = (1/3 BC)/(BC) = 1/3`

⇒ ar(ΔBDE) = `24/3`

= 8 cm²