Problem list（16 problems）
- Area of the trapezoid? The "÷2" in the formula is there because flipping a second copy of the trapezoid makes a parallelogram
- Area of the circle? π is simply "how many radius-squares fit in a circle"
- Volume of the cone? Any pointed solid is one third of the prism with the same base and height — pyramids and cones alike
- Sum of the interior angles of a hexagon? The formula is 180 × (corners − 2)
- How many degrees is angle x? The angles of a triangle add to 180° because cutting them off and lining them up makes a straight line
- How many degrees is angle x? "Vertically opposite angles are equal" is not a rule to memorise — you can rebuild it from "a straight line is 180°"
- How many diagonals can be drawn in total? Count from one corner, multiply by the number of corners, then halve
- Area of the rhombus? Any quadrilateral whose diagonals cross at right angles (rhombus, square, kite) obeys this same formula
- Area of triangle ABC? Either diagonal halves it — parallelogram, rectangle, rhombus or square, it makes no difference
- What is the total surface area? For surface area, do not count six separate faces — see three pairs of identical faces
- How many degrees is angle x? "Exterior angle = sum of the two non-adjacent interior angles
- Volume of the cylinder? Cylinders and prisms alike are "base area × height"
- Volume of the cuboid? "Base area × height" works for any prism — square, triangular, or circular
- Area of the sector? "Arc × radius ÷ 2" works without knowing the central angle
- Area of triangle ABC? "See 30°, halve the slanted side
- What is the perimeter of the hexagon? 3
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
- Write the same thing two different ways
- Fold it, turn it, copy it across