Geometry › Shapes

Shapes

A shape is a closed figure made from straight lines or curves. Each one has its own name, sides and rules.

Shape sorter

Drag each shape into the right bin. 0/8 sorted.

Shapes pile

Square

Rectangle

Hexagon

Circle

Trapezium

Octagon

Triangle

Pentagon

3 sides

4 sides

5+ sides

Round

Polygons

A polygon is a closed shape made of straight sides only. Triangles, squares, pentagons and hexagons are all polygons. Circles are not — their boundary is a curve.

Naming polygons

3 sides — triangle
4 sides — quadrilateral (square, rectangle, rhombus, trapezium…)
5 sides — pentagon
6 sides — hexagon
8 sides — octagon
n sides — n-gon

Regular vs irregular

A regular polygon has all sides the same length and all angles equal. A regular triangle is equilateral. A regular quadrilateral is a square. Irregular polygons just don't have that uniformity.

Sum of interior angles

For a polygon with n sides, the interior angles always add up to (n − 2) × 180°. So a pentagon's angles sum to 540°, a hexagon's to 720°.

Quadrilateral family

Square — 4 equal sides, 4 right angles.
Rectangle — 4 right angles, opposite sides equal.
Rhombus — 4 equal sides, but angles need not be right.
Parallelogram — both pairs of opposite sides parallel.
Trapezium — at least one pair of parallel sides.