Points X and Y lie on sides AB and AC respectively of triangle ABC. If AB=7, AC=10, AX=4 and AY=6, what is the ratio of the area of triangle AXY to the area of triangle ABC?
Area of ABC = (1/2) (AB) (BC) sin (BAC) (1)
Area of AXY = (1/2) (AX) ( AY) sin (BAC) (2)
Dividing ( 2) by (1) we will "cancel" (1/2) and sin (BAC) ...so we get
AX * AY 4 * 6 24 12
________ = ______ = ___ = ____
AB * BC 7 * 10 70 35
+46 
