In a triangle ABC with area 60 cm², G is the centroid. What is the area of triangle GBC?
20 cm²
The centroid G of triangle ABC divides the triangle into three smaller triangles of equal area: △GAB, △GBC, and △GCA.
This is because the medians from each vertex pass through G, and the centroid divides each median in the ratio 2 : 1, which makes the three triangles formed by joining the centroid to the vertices equal in area.
Calculation:
\(\text{Area of } \triangle GBC = \dfrac{1}{3} \times \text{Area of } \triangle ABC\)
\(= \dfrac{1}{3} \times 60 = 20 \text{ cm}^2\)
Hence the area of triangle GBC is 20 cm².
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