Question

The midpoints of sides AB, BC, and AC in ∆ABC 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 ∆ABC is 1440 sq cm, then the area, in sq cm, of ∆XYZ is

Answer 1

Correct Answer: 90

In any triangle, the medians divide the triangle into six smaller triangles of equal area. The area of the medial triangle formed by the midpoints of the sides of the original triangle (in this case, △XYZ) is exactly one-fourth of the area of the original triangle. Since the area of △ABC is given as 1440 sq cm, the area of △XYZ, which is the medial triangle, is:
Area of △XYZ= 14×1440=360 sq cm
However, we must consider the area of the triangle formed by the medians, which is half the area of the medial triangle. Therefore, the area of △XYZ
is: {90} sq cm