Area of triangles, parallelograms, trapezia and circles
Move pieces to see why the area of a parallelogram is base × height, why a triangle is half of that, complete a trapezium with a copy of itself, and estimate the area of a circle.
- UK: Year 6
- France: grade 5
- Germany: grade 5
- Iran: grade 4
- Afghanistan: grade 6
- Syria: grade 5
- Palestine: grade 5
- Ukraine: grade 6
- Russia: grade 4
Guide
This studio follows the cut-and-move method of the Iranian grade 4 to 6 books: cut a triangle off a parallelogram and slide it across to make a rectangle; two equal triangles make a parallelogram; two equal trapezia make a parallelogram; and the area of a circle is estimated by counting squares. In England, parallelograms and triangles are Year 6; trapezia and circles come later (Key Stage 3).
Drag a piece to move it; the ↺ and ↻ buttons give it a quarter turn. With a keyboard, move to a piece and use the arrow keys. Each piece must fit exactly into the dashed gap.
The height is always at right angles to the base. Common mistakes are to multiply by the slanted side instead of the height, and to forget to halve for a triangle. Moving the pieces shows that the area does not change.