What is a parallelogram?
A parallelogram is a four-sided shape whose opposite sides are parallel and the same length.
The answer
A parallelogram has 4 sides, 4 vertices and 2 pairs of parallel sides. The one drawn here has 0 lines of symmetry. Special parallelograms have more: a rhombus and a rectangle have 2, a square has 4. The angles inside a parallelogram add up to 360°.
Parallelogram diagram and properties
| Property | Count |
|---|---|
| Sides | 4 |
| Vertices (corners) | 4 |
| Angles add up to | 360° |
| Right anglesA rectangle is a parallelogram with 4. | 0 |
| Pairs of parallel sides | 2 |
| Lines of symmetrySpecial parallelograms have more: a rhombus and a rectangle have 2, a square has 4. | 0 |
Key facts about the parallelogram
- Opposite angles are equal, and angles next to each other add up to 180°.
- Area = base × perpendicular height. The height is measured straight up at a right angle, not along the sloping side.
- Rectangles, squares and rhombuses are all special parallelograms.
- It has no lines of symmetry unless it is a rectangle or a rhombus (which have 2) or a square (4). Every parallelogram looks the same after a half turn.
Where you see it
The shape of a pushed-over box, some car park spaces drawn at an angle, and the pattern on a lot of tiled floors.
The common mistake
Thinking a parallelogram has two lines of symmetry. Fold one along either diagonal and the halves do not match. Tracing it and flipping the tracing shows this quickly.
An 11+ style question
One angle of a parallelogram is 65°. What are the other three angles?
Answer: 115°, 65° and 115°
- Angles next to each other in a parallelogram add up to 180°, so the angle beside the 65° is 180 − 65 = 115°.
- Opposite angles are equal, so the other two are 65° and 115°.
- Check: 65 + 115 + 65 + 115 = 360.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a parallelogram have?
A parallelogram has 4 straight sides and 4 vertices (corners). Its angles add up to 360°.
How many lines of symmetry does a parallelogram have?
A parallelogram like the one drawn here has 0 lines of symmetry. Special parallelograms have more: a rhombus and a rectangle have 2, a square has 4.
Is a rectangle a parallelogram?
Yes. A rectangle has two pairs of parallel sides, with opposite sides equal, so it is a parallelogram. It is a special one, because all four of its angles are right angles.
How do you find the area of a parallelogram?
Multiply the base by the perpendicular height. A parallelogram with a base of 8 cm and a height of 5 cm has an area of 40 cm². Year 6 children learn this, and it is why you never multiply by the sloping side.
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.