Polygons and angle sums
Find the regular polygons, discover the angle sum of a triangle, and split polygons into triangles to find their angle sums.
- UK: Year 5
- France: grade 5
- Germany: grade 7
- Iran: grade 5
- Afghanistan: grade 5
- Syria: grade 6
- Palestine: grade 4
- Ukraine: grade 5
- Russia: grade 8
Guide
This studio is for Years 5 and 6.
A regular polygon has all its sides equal and all its angles equal. A rhombus has only equal sides and a rectangle only equal angles, so neither is regular. A square is regular.
The angles of every triangle add up to 180°. A classic demonstration: tear the corners off a paper triangle and put them side by side; they make a straight line. On the board, children draw several triangles and read their angles.
For a polygon, draw all the diagonals from one vertex. A quadrilateral splits into 2 triangles, a pentagon into 3 and a hexagon into 4, so the angle sums are 2 × 180, 3 × 180 and 4 × 180. A common slip is to split from a point in the middle, which also counts the full turn round that point.