geometry - triangles and subsets of the plane

[mbbx3adr]

A subset S of the plane has the property that the area of any triangle ABC with vertices A, B and C all in S is less than 1.

Prove that there exists a triangle of area 4 which contains the whole set S.

 

[pka]

A subset S of the plane has the property that the area of any triangle ABC with vertices A, B and C all in S is less than 1.
Prove that there exists a triangle of area 4 which contains the whole set S.

I have some questions. Is this a question in a topology course?
That is, can we assume that the set S is bounded?

Most important are you sure it does not say rectangle and not triangle?
If the closure of S is compact, I found a rectangle of area 4 the closure of which contains S.

 

[mbbx3adr]

no, it isn't a topology course. i have never done topology. it is definately a triangle and not a rectangle. thank you for any help.

i have been able to show that there is a triangle of area 4 which contains the whole set S when the subset of S is a certain shape. E.g. when the subset S is a rectangle or a circle. but not sure how to prove this when S is any shape.