Question

In an equilateral trnangle ABC, D is the mid-point of AB and E is the mid point of AC. Then ar (ΔABC) : ar (ΔADE) = ______.

Answer 1

In an equilateral trnangle ABC, D is the mid-point of AB and E is the mid point of AC. Then ar (ΔABC) : ar (ΔADE) = 4 : 1.

Explanation:

D and E are midpoints so `AD = (AB)/2` and `AE = (AC)/2`. 

Triangle ADE is similar to triangle ABC with linear scale factor `1/2`, so its area is `(1/2)^2 = 1/4` of area (ABC). 

Therefore ar (ΔABC) : ar (ΔADE) = 4 : 1.