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Ratio of mid-point triangle area

CMAT 2021 · Quantitative Techniques & Data Interpretation · Easy · Geometry

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In a △ABC\triangle ABC, DD, EE and FF are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a △DEF\triangle DEF and the area of a △ABC\triangle ABC is:

  1. A.

    1:4

  2. B.

    1:2

  3. C.

    2:3

  4. D.

    4:5

Answer

A

Explanation

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 14\frac{1}{4} of the main triangle's area.

Thus, Area(△DEF):Area(△ABC)=1:4\text{Area}(\triangle DEF) : \text{Area}(\triangle ABC) = 1 : 4.

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