Shape, Space & Angles

Shape, space and angles

This topic covers 2D and 3D shapes, angles and symmetry — all common in the 11+.

Angles

• A right angle = 90° (a square corner).
• Angles on a straight line add up to 180°.
• Angles around a point add up to 360°.
• Types: acute (< 90°), right (90°), obtuse (between 90° and 180°), reflex (> 180°).

Triangles

• The angles in a triangle always add up to 180°.
• Equilateral: all sides and angles equal (each 60°).
• Isosceles: two equal sides and two equal angles.
• Scalene: all sides and angles different.
• Right-angled: has one 90° angle.

Quadrilaterals (4-sided shapes)

The angles add up to 360°.

• Square: 4 equal sides, 4 right angles.
• Rectangle: opposite sides equal, 4 right angles.
• Parallelogram: opposite sides parallel and equal.
• Rhombus: 4 equal sides, opposite angles equal.

Perimeter, area and volume

• Perimeter = distance around the edge (add all sides).
• Area of a rectangle = length × width (in square units).
• Area of a triangle = ½ × base × height.
• Volume of a cuboid = length × width × height (in cubic units).

Symmetry

• A line of symmetry divides a shape into two matching halves (a square has 4).
• Rotational symmetry: how many times a shape looks the same when turned once round (a square has order 4).

3D shapes

Count faces (flat surfaces), edges (where faces meet) and vertices (corners). A cube has 6 faces, 12 edges, 8 vertices.

Worked example

Two angles on a straight line are 120° and x. Find x.

• Angles on a straight line add to 180°, so x = 180 − 120 = 60°. ✓

Common mistakes

• Forgetting the angle facts (straight line 180°, point 360°, triangle 180°).
• Muddling area (square units) with perimeter (a length).
• Miscounting faces, edges and vertices of 3D shapes.

Top tips

• Learn the three key angle facts — they solve most angle questions.
• Remember triangle angles sum to 180° and quadrilaterals to 360°.
• Use the right units: cm for perimeter, cm² for area, cm³ for volume.

Quick recap

• Angle facts: straight line 180°, point 360°, triangle 180°, quadrilateral 360°.
• Triangles (equilateral/isosceles/scalene) and quadrilaterals (square/rectangle/parallelogram/rhombus).
• Perimeter = around, area = inside (units²), volume = inside a solid (units³); know symmetry and 3D faces/edges/vertices.