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G is the centroid of triangle ABC, whose area is $96 cm^{2}$ . What is the area of triangle BGC?

Competition practiceGeometry

A $24 cm^{2}$
B $48 cm^{2}$
C $32 cm^{2}$
D $16 cm^{2}$

Step-by-Step Solution

The centroid splits the triangle into three equal triangles GBC, GCA, GAB:

\frac{96}{3} = 32 cm^{2}

.

Answer: C)

32 cm^{2}

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