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On triangle ABC, D and E are the midpoints of BC and AB respectively. The median AD meets CE at F. If the are of the triangle EFA is 1 square cm., what is the area of triangle ABC?

Sagot :

Property:  The medians of a triangle divide the triangle into 6 parts with equal areas.

Step 1:  Draw the remaining median from vertex B to the midpoint of its opposite side/segment AC.

The three medians of ΔABC with centroid at F now divide the triangle into 6 equal parts.

Step 2:  Given that the area of one of the 6 triangle formed by the medians, Δ EFA, is 1 cm², solve for the area of Δ ABC:

Area of Δ ABC = 6 (1 cm²)
Area of Δ ABC = 6 cm²           

ANSWER:  The area of Δ ABC is 6 cm².

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