Question

In the following, DE || BC. If DE = 6 cm, BC = 12 cm, find the ratio of Area (ΔADE) and Area (quad. DECB).

Answer 1

Given: DE || BC, DE = 6 cm, BC = 12 cm.

Step-wise calculation:

1. Because DE || BC, ΔADE ~ ΔABC (corresponding sides proportional).

The ratio of corresponding linear sides = `(DE)/(BC)`

= `6/12`

= `1/2`

2. Ratio of areas of similar triangles = (Ratio of sides)².

⇒ `(Area(ΔADE))/(Area(ΔABC)) = (1/2)^2`

= `1/4`

3. Quadrilateral DECB is the part of ΔABC outside ΔADE, so

Area (DECB) = Area (ΔABC) – Area (ΔADE) = `(1 - 1/4)`

Area (ΔABC) = `3/4` Area (ΔABC)

4. Therefore `(Area (ΔADE))/(Area(DECB)) = (1/4)/(3/4) = 1/3`.