# Area Problem #18

Lines have been drawn such that the 1/3 points of each side meet their opposite vertex.
If the area shaded green is 63cm2, what is the total area of the triangle ABC?

## 13 thoughts on “Area Problem #18”

1. ProfSmudge says:

Thanks for your reply. The GeoGebra demo is very neat, but I don’t think it is near to a proof, is it? I think it is just a demonstration of something we know to be true. For example, how do we know that when we join a vertex A of the inner triangle ABC to a midpoint of a ‘nearby’ side of the outer triangle, that the resulting line segment is parallel to the side BC ?

• it is in fact a proof. You can find it in:
W. Johnston and J. Kennedy, Heptasection of a triangle, Mathematics Teacher, 8b (1993), p.192

2. Andy Wright says:

Is it 73.5? (I actually make it 73.49999, but that’s floating point for you)

3. Amir says:

It might seem really obvious, but where do I begin with this?

• Start messing with pythagoras formula, area of triangle formula and perimeter formula

• Amir says:

Area of triangle formula as in 1/2 x b x h or 1/2 ab sin C?

• it’s a right angled triangle so they’re one in the same.

4. Amir says:

I’ve played around in Geogebra and got the relationship between the area of the white part and the whole triangle, and then got 73.5 as an answer… cheating, no?

• Qamar says:

In case of overlap triangles in a triangle,
Area of triangle ABC =63 sq cm,