Covering an Isosceles Right Triangle
It is relatively easy to completely cover an isosceles right triangle with two non-overlapping congruent shapes. It is also easy to do so using four non-overlapping congruent shapes.
(see the diagram below)
It is not so easy to cover an isosceles right triangle with three non-overlapping congruent shapes. In fact, it is impossible! But you can cover most of it.
Your challenge: Find the shape that will best cover an isosceles right triangle with three non-overlapping congruent copies, and calculate the maximum fraction of the triangle you can cover using that shape.