Composite Figures (Overlap and Difference)

The part made where two curves overlap gets pulled out. A leaf shape in the middle of two overlapping quarter circles, the wings outside it, the four corners left outside a circle inscribed in a square, a crescent on the two legs of a right triangle: the ground covered by shapes that can only be expressed through overlap and difference is found, as calculation.

In drawings asking for an overlapping part, papers turn up that stopped once the two quarter circles were added. Where only the inside of the square is colored, the answer can never exceed the area of the square. Exceed it and the stage subtracting what spills over is still owed.

The shapes handled in Area of a Circle end here, and what carries over is the way of assembling by splitting a shape and adding or subtracting. In Volume of Prisms and Cylinders one further step is added to the ground found by that assembly: multiplying by the height.