medians of triangle ABC intersect at G. if ar(triangle ABC) = 27 CM^2, then ar(triangle BGC) =?
To find the area of triangle BGC, we can use the fact that the medians of a triangle divide it into six equal parts.
Since the medians of triangle ABC intersect at G, the area of triangle BGC is equal to 1/6th of the area of triangle ABC.
Therefore, to find the area of triangle BGC, we need to divide the area of triangle ABC by 6.
Given that the area of triangle ABC is 27 cm^2, we can calculate the area of triangle BGC as follows:
Area of triangle BGC = (1/6) * Area of triangle ABC
= (1/6) * 27 cm^2
= 4.5 cm^2
So, the area of triangle BGC is 4.5 cm^2.
Area of triangle = bh/2
Medians meet at one third from the base, so h'=h/3. Therefore triangles with the vertex at G is one third the area of the whole triangle, or 27/3=9 cm².