Point E is the midpoint of the side BC of triangle ABC and F is the midpoint of AE. The line through BF intersects AC at D. Find the area, in cm squared, of triangle AFD if the area of the triangle is 48 cm2
+128460 See the following image :
Note that triangles BEF and BGD are similar
So
EF/BE = GD/BG
4/6 = GD/8
GD = 8*4/6 = 32/6 = 16/3
And GD is the altitude of triangle BDC
And the area of this triangle = (1/2)(BG)(GD) = (1/2)(8)(16/3) = 64/3 units^2 (1)
And the area of triangle BFA = area of triangle BEA - area of triangle BEF =
Area of triangle BEA = 24
Area of triangle BEF = (1/2) of area of triangle BEA =12
So area of triangle BFA =24 - 12 =12
So.... area of triangle AFD =
Area of triangle ABC - area of triangle BDC - area of triangle BFA = 48 - 64/3 - 12 = 36 - 64/3 =
[108 -64] / 3 = 44/3 units^2
