The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and

Question

The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of $$	riangle XYZ$$ is

Accepted Answer

The question describes a figure of the following nature, We are told that the area of the triangle ABC is 1440. By proportionality theorem, the area of MPN should be one fourth of that. Since we know that, ( A r e a △ 1 ) A r e a △ 2 = ( s i d e o f △ 1 ) 2 ( s i d e o f △ 2 ) 2 \frac{\left(Area\

The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of △XYZ\triangle XYZ△XYZ is

The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of $\triangle XYZ$ is