Pentominoes for School Maths Lab

Quick Answer: Pentominoes are the twelve different flat shapes that can be made by joining five equal squares edge to edge. A pentominoes set is used in maths lessons on area, perimeter, symmetry and spatial reasoning, and for the classic puzzle of fitting all twelve pieces into a rectangle.

Twelve Shapes, Five Squares Each

If rotations and reflections count as the same shape, there are exactly twelve pentominoes. They are usually named after the letters they resemble: F, I, L, N, P, T, U, V, W, X, Y and Z. Finding all twelve is a worthwhile investigation in itself, because students have to decide when two arrangements are really one shape turned over.

Every piece has an area of five squares, but the perimeters are not all equal. Eleven of the twelve have a perimeter of 12 units, while the P-shaped piece, which contains a 2 × 2 block, has a perimeter of 10. That makes the set a direct counter-example to the belief that shapes with the same area must have the same perimeter.

Together the twelve pieces cover 60 squares, so they can be arranged into rectangles of 6 × 10, 5 × 12, 4 × 15 or 3 × 20. Solving these puzzles builds visualisation and persistence. How many complete sets come with this product, and their material and colours, should be confirmed with LabEquip.

Care & Handling

• Keep each full set in its own bag or tray, so an incomplete set is noticed before a puzzle lesson.
• Clean according to the material: plastic pieces can be washed in mild soapy water, while wooden pieces should only be wiped.
• Store the pieces flat and away from heat so they stay square and fit neatly in puzzles.

Applications

• Comparing area and perimeter: every piece has an area of 5, but a perimeter of 10 or 12
• Sorting the pieces by their number of lines of symmetry
• Tiling rectangles such as 6 × 10 with all twelve pieces
• Testing which pieces fold into a cube with the top left open

Specifications

Why Choose LabEquip

Teachers who use Colour Tiles for area and perimeter work often move on to pentominoes, where the five-square rule turns counting into a puzzle. LabEquip lists both in the Mathematics School Lab Products range, and the contact page takes enquiries for maths clubs and class sets.

Frequently Asked Questions

Why are there exactly twelve pentominoes?

Twelve is the number of different ways to join five equal squares edge to edge when a shape that has only been turned or flipped is counted once. Students can check this by drawing every arrangement on squared paper and crossing out duplicates.

Do all pentominoes have the same perimeter?

No. All have an area of five squares, but eleven have a perimeter of 12 units and one, the P-pentomino, has a perimeter of 10, because its 2 × 2 block hides more shared edges. It is a simple proof that equal area does not mean equal perimeter.

Which pentominoes have lines of symmetry?

The X-pentomino has four lines of symmetry and the I-pentomino two. T, U, V and W each have one. The remaining six, F, L, N, P, Y and Z, have no line of symmetry, although Z has rotational symmetry of order 2.

What rectangles can be made with a full set?

The twelve pieces cover 60 squares, so the rectangle must have an area of 60: 6 × 10, 5 × 12, 4 × 15 and 3 × 20 are all possible. The 3 × 20 version is the hardest, with very few solutions, while the 6 × 10 has a great many.

Can pentominoes be folded into boxes?

Some can. If a pentomino drawn on paper folds into a cube without a lid, it is the net of an open box. Eight of the twelve work, and students can predict which ones before cutting them out, which links the set to work on nets.

What age group uses pentominoes?

Upper primary students use them for area, perimeter and symmetry, and the rectangle puzzles challenge secondary students and adults. Because the rules are simple, one set works well for mixed-ability groups and maths clubs.

Last Updated: September 2026