You've probably seen this shape before. It is several straight lines whose outline seems to be curved. For some number n, connect the following pairs of points with segments:

(1,0) and (0,n)
(2,0) and (0,n-1)
(3,0) and (0,n-2)
...
(n,0) and (0,1)

Within the picture formed there are n simple triangles, those without segments cutting through them.

Prove: these triangles all have the same area.

There are also n simple quadrilaterals, each sharing two sides with the triangles.

Prove: these quadrilaterals all have the same area.

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