In the triangle ABC, point M is the midpoint of AB, point D belongs to AC so that AD:DC=2:5. If the Area of ABC = 56 yd^2, find the Area of BMC, Area of AMD, and the Area of CMD.

Answer 1

Since M is the midpoint,
area AMC = area BMC , they have the same height and base
so BMC = (1/2)(56) = 28

now look at triangles AMD and CMD, they have the same height and their bases are in the ratio of 2 : 5

so triangle AMD = (2/7)(28) = 8
and triangle CMD = (5/7)(28) = 20