Points X and Y lie on sides AB and AC respectively of triangle ABC. If AB=7, AC=10, AX=4 and AY=8, what is the ratio of the area of triangle AXY to the area of triangle ABC?
A
4
X
8 10
7
Y
B C
Area of ABC = (1/2) ( AB) (AC) sin BAC = (1/2) ( 7)(10) sin BAC
Area of AXY = (1/2) (AX) ( AY) si BAC = (1/2) (4) ( 8) sin BAC
[ AXY ] / [ ABC ] = (4 * 8 ) / ( 7 * 10) = 32 / 70 = 16 / 35
