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G is the centroid of a triangle ABC whose area is $72 cm^{2}$ , and D is the midpoint of BC. What is the area of triangle GBD?

Competition practiceGeometry

A $12 cm^{2}$
B $24 cm^{2}$
C $18 cm^{2}$
D $8 cm^{2}$

Step-by-Step Solution

The three medians cut the triangle into six small triangles of equal area, and GBD is one of them:

\frac{72}{6} = 12 cm^{2}

.

Answer: A)

12 cm^{2}

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