Question

Points $D$, $E$, and $F$ are the midpoints of sides $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively, of $\triangle ABC$. Points $X$, $Y$, and $Z$ are the midpoints of $\overline{EF}$, $\overline{FD}$, and $\overline{DE}$, respectively. If the area of $\triangle XYZ$ is 21, then what is the area of $\triangle CXY$?

Answer 1

XY = 1/4 AB
altitude of CXY is 3/4 the altitude ABC.

So, CXY has area 1/3 * 3/4 * 21 = 21/4

Answer 2

It's not 21/4

Answer 3

Its 63. Steve's logic is mostly right, except the area of triangle XYZ is 21, not the area of ABC.