Question

In the adjoining figure, BD = 2CD. If area of ΔABC = 36 cm², find the area of ΔABD.

Answer 1

Given:

In the adjoining figure, D lies on BC with BD = 2CD.

Area (ΔABC) = 36 cm².

Triangles ABD and ACD share the same altitude from A to line BC.

Step-wise calculation:

1. Because ΔABD and ΔACD have the same vertex A and their bases BD and DC lie on the same line BC.

Their areas are proportional to their bases: 

Area (ΔABD) : Area (ΔACD)

= BD : DC

= 2 : 1

2. Let Area (ΔACD) = x cm².

Then Area (ΔABD) = 2x cm².

3. Area (ΔABC)

= Area (ΔABD) + Area (ΔACD) 

= 2x + x

= 3x

4. Set 3x = 36

⇒ x = 12

5. Therefore, Area (ΔABD) 

= 2x

= 24 cm²