Problem list（13 problems）
- Area of the overlap? "Sum of the sheets − what you see = the overlap
- What area of the table is covered by paper? Overlap problems are really about how many times each region got counted
- Area of the overlap? "Add them up, then subtract the excess
- How much larger is イ than ア? When a problem asks for a difference, you may add or subtract the same thing from both sides — which lets you delete an awkward shared region without ever computing it
- Area of the red part? "Take the whole, subtract what you don't want
- Area of the red part? With scattered sectors, add up the central angles first
- Area of this shape? Most area problems have two or more routes
- Area of this triangle? For any slanted shape: box it in, then subtract the right triangles around it
- Area of the inner square? A tilted square is "the boxing square minus the four corner triangles"
- Area of the square? Chasing the side length is a dead end at elementary level
- Area of the red part? This shape is called the "shoemaker's knife"
- Total area of the two crescents? Found by Hippocrates 2,200 years ago
- What is the total area of the three sectors? When the parts cannot be found one by one, look only at the total
Other ideas
- Shearing — moving a shape without changing its area
- Ratios — answers without fixing a single number
- 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
- Write the same thing two different ways
- Fold it, turn it, copy it across
- Back to why the formula works