Medians and Areas

Geometry Level 2

In triangle $ABC$ , two medians are drawn: $BE$ and $CF$ . They intersect at point $G$ . If the area of $ABC$ is 24, what is the area of the quadrilateral $AFGE$ ?

6 12 8 9

1 solution

A Former Brilliant Member
Nov 14, 2017

A median divides a triangle into two equal areas. Draw another median $AH$ . The three medians of a triangle are concurrent. The three medians divide the triangle into six equal areas. So the area of one small triangle is $\dfrac{24}{6}=4$ . Since quadrilateral $AFGE$ is composed of the triangles of equal areas, its area is $2\times 4=\boxed{8}$

Note: The figure is not drawn to scale.

Medians and Areas

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