Let A,B,C be the mid-points of sides XY,YZ and XZ, respectively of ΔXYZ. If the area of ΔXYZ is 8464 cm
2
, then find the area (in cm
2
) of ΔABC.

By joining the midpoints of the three sides of a triangle, the main triangle is divided into four smaller triangles of equal area.
Therefore, the area of the midpoint triangle ΔABC is exactly one-fourth of the total area of ΔXYZ:

Area of ΔABC=
4
1
​
×Area of ΔXYZ
Area of ΔABC=
4
8464
​
=2116 cm
2