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

Question

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

Steve · Answer

XY = 1/4 AB altitude of CXY is 3/4 the altitude ABC. So, CXY has area 1/3 * 3/4 * 21 = 21/4

pshhhh · Answer

It's not 21/4

asdfjkl; · Answer

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