Question

In a $	riangle ABC$, $D$, $E$ and $F$ are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a $	riangle DEF$ and the area of a $	riangle ABC$ is:

Accepted Answer

A. By the mid-point theorem, joining the mid-points of the three sides of a triangle divides the triangle into four smaller congruent triangles, each having area equal to $\frac{1}{4}$ of the main triangle's area. Thus, $	ext{Area}(	riangle DEF) : 	ext{Area}(	riangle ABC) = 1 : 4$.

Ratio of mid-point triangle area

Explanation

Practise this under exam conditions