Question

In triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC ?

• A. 1 : 2
• B. 1 : 3
• C. 2 : 3
• D. 1 : 4

Answer 1

Answer:

B. 1 : 3

We use a key centroid property:

The three medians divide the triangle into 6 smaller triangles of equal area.

So:

• Total area of ( \triangle ABC = 6) equal parts

• Each small triangle has area (= \frac{1}{6}) of (ABC)

Now, ( \triangle GAB ) is made up of 2 of those equal small triangles.

So:
$\text{Area}(GAB) = \frac{2}{6} = \frac{1}{3} \text{ of } ABC$

Final Answer:

$\boxed{1:3}$