Suppose you had two stained-glass tiles in the shapes of polygons and you laid them on top of each other. Their overlapping area also forms a polygon, like the ones I have shown in the image:
Notice how the blue squares overlap to form a triangle, the green triangles overlap to form a quadrilateral, and the orange polygons overlap to form two disjoint polygons: a triangle and a quadrilateral. Here is your challenge:
- Overlap a triangle and a square to form a septagon.
- Overlap a triangle and a quadrilateral to form an octagon.
- Overlap two quadrilaterals to form two disjoint polygons: one septagon, and one quadrilateral.
- Overlap two quadrilaterals to form a decagon.
- Overlap two hexagons to form a 16-gon.
Remember that the polygons need not always be convex!