Grade 5

Same height, different base

Two triangles leaning on the same line share a height, so their areas follow their bases -- once you see which segment is which.

1
Three parts to one
In triangle ABC, point M lies on side BC so that BM is three times as long as MC. The area of the whole triangle is $200\text{ cm}^2$ . What is the area of triangle ABM?
2
Work backwards
In triangle ABC, point M lies on side BC so that BM is three times as long as MC. The area of triangle AMC is $45\text{ cm}^2$ . What is the area of triangle ABC?
3
Past the corner
Triangle ABC has area $250\text{ cm}^2$ . Point D lies on the line through B and C, beyond C, so that BD is one and a half times BC. What is the area of triangle ACD?