Problem list（11 problems）
- How long is the line from B down to AC? Write the same area two ways — with two different base-and-height pairs — and set them equal
- a + b + c = ? Count the same area two ways — split into three, and all at once
- Area of this shape? Most area problems have two or more routes
- Area of the overlap? "Sum of the sheets − what you see = the overlap
- Volume of the stone? However complicated the shape, sinking it in water measures its volume — the very thing Archimedes noticed in his bath
- What is the largest area it can enclose? The same perimeter can enclose wildly different areas
- What is the perimeter of the hexagon? 3
- The circle's area is what percentage of the square's? When a question asks for a percentage, try writing the side as a letter
- Area of trapezoid ABCD? It is no accident that 9 and 25 are square numbers
- What is the side of the square? If the legs are a and b, the inscribed square's side is always a×b÷(a+b)
- Area swept by the square? "I cannot find the length, but I can find length × length
Other ideas
- Shearing — moving a shape without changing its area
- Ratios — answers without fixing a single number
- Add, then subtract — an overlap is a counting problem
- Circles and sectors — multiply by π once, at the very end
- Chasing angles — there are only four tools
- Decide how to count, then count
- Flatten the solid before you think about it
- Fold it, turn it, copy it across
- Back to why the formula works