Üçgende Alan ve Ağırlık Merkezi

3.

[IMAGE DESCRIPTION: A large triangle ABC with points D and E on the sides AB and AC. A shaded triangle DEG with G as the centroid.]

Şekildeki ABC üçgeninde G ağırlık merkezi, D ve E bulundukları kenarların orta noktalarıdır.

DEG üçgeninin alanı 12 birimkare olduğuna göre, ABC üçgeninin alanı kaç birimkaredir?

A) 72 B) 96 C) 108 D) 144 E) 216

Soruda görsel içerik var: A large triangle ABC is depicted with vertex A at the top. Points D and E are located on the sides AB and AC respectively, such that D is the midpoint of AB and E is the midpoint of AC, indicated by tick marks on the segments AD, DB, AE, and EC. A point G is inside the triangle, acting as the centroid of triangle ABC. A smaller shaded triangle DEG is formed by connecting the midpoints D and E to the centroid G. The base BC is horizontal at the bottom.