What does pi (π) mean?

Pi is the number of times a circle’s diameter fits around its edge, a little more than 3. It is written π and starts 3.14159, with digits that never end. The same is true of every circle, from a coin to a wheel. The circle levels here count π as 3, so a circle 10 cm across is about 30 cm around, and every answer stays whole.

How do you find the missing angle in a triangle?

Subtract the two angles you know from 180°, because the three angles inside any triangle always add up to 180°. With 54° and 67°, the known angles make 121°, and 180 − 121 = 59, so the third angle is 59°. If your answer comes out at 0 or below, recheck your sum, since every angle in a triangle is bigger than 0°.

How do you remember the angle sum of a polygon?

Split the polygon into triangles from one corner, then count them. A shape with n sides always splits into n − 2 triangles, and each one holds 180°. A hexagon has 6 sides, so it makes 4 triangles, and 4 × 180 = 720°. The rule (n − 2) × 180° then works for any polygon whose straight sides do not cross.

Why does my child mix up area and perimeter?

Children mix them up because, for a rectangle, both come from the same two side lengths: perimeter adds all four sides, while area multiplies two of them. A card 6 cm by 4 cm is 20 cm around but covers 24 cm². Ask your child to trace the edge with a finger for perimeter, then colour in the inside for area.

How can a teacher bring this geometry practice into class, and is it free?

A teacher pays nothing: pupils open every level in a browser, and nobody registers or installs anything. On squared paper or the board, pupils draw every rectangle with an area of 24 squares. Then they find each perimeter: 1 by 24 gives 50, 2 by 12 gives 28, 3 by 8 gives 22 and 4 by 6 gives 20. For a dashboard of which pupils are improving, add the schools plan, billed per student.

Math practice · reimagined

Geometry Game

This geometry challenge goes from a rectangle’s perimeter to finding a circle’s radius in its equation, and π counts as 3, so no answer ever needs a decimal point. Each shape is a race with your rival, and only the first right number hits.

Ages 4–99+ · no download · plays in your browser · 23 languages

Choose your level ▸

What is geometry?

Geometry is the part of math that measures shapes and space. It asks how far it is around a shape, called its perimeter, and how much flat space it covers, called its area. Volume tells how much a box or a ball holds. Angles measure turns in degrees, written °, and a square corner is exactly 90°.

Every level of Geometry

Example: the area of a 12 by 8 rectangle

Area counts how many 1 by 1 squares cover a shape, so for a rectangle you multiply the two sides: 12 × 8.
Split the 12 to make it easier: 10 × 8 = 80 and 2 × 8 = 16.
Add the two parts, 80 + 16 = 96, and type 96.

Learn it step by step

The perimeter is the distance all the way AROUND a shape — like walking the fence around a garden.

For a rectangle, add up all four sides. A 5 by 3 rectangle has sides 5, 3, 5, 3, so the perimeter is 5 + 3 + 5 + 3 = 16. (A shortcut: add length and width, then double.)

Type the total distance around.

Tips and common mistakes

Read the unit for a clue: perimeters are in cm, areas in cm² and volumes in cm³. The small raised number counts how many lengths were multiplied together.
A common mistake is mixing up radius and diameter. Check which the problem gives: d goes all the way across, and r goes from the centre out, half as far.
Away from the screen, measure a book, a table and a door in centimetres or metres, then work out each one’s perimeter and area together.

How to play

Early levels play like an area and perimeter game, with lines such as Area of 12×8; later ones add angles and solids, like Cone r=3 h=6, volume=? (π≈3). Key in the answer, pressing minus for some midpoints and slopes. Pea Pod strikes only when your answer arrives first, and a quick answer weighs more than a slow one.

— Quick answers —

Geometry: the short FAQ

What does pi (π) mean?: Pi is the number of times a circle’s diameter fits around its edge, a little more than 3. It is written π and starts 3.14159, with digits that never end. The same is true of every circle, from a coin to a wheel. The circle levels here count π as 3, so a circle 10 cm across is about 30 cm around, and every answer stays whole.
How do you find the missing angle in a triangle?: Subtract the two angles you know from 180°, because the three angles inside any triangle always add up to 180°. With 54° and 67°, the known angles make 121°, and 180 − 121 = 59, so the third angle is 59°. If your answer comes out at 0 or below, recheck your sum, since every angle in a triangle is bigger than 0°.
How do you remember the angle sum of a polygon?: Split the polygon into triangles from one corner, then count them. A shape with n sides always splits into n − 2 triangles, and each one holds 180°. A hexagon has 6 sides, so it makes 4 triangles, and 4 × 180 = 720°. The rule (n − 2) × 180° then works for any polygon whose straight sides do not cross.
Why does my child mix up area and perimeter?: Children mix them up because, for a rectangle, both come from the same two side lengths: perimeter adds all four sides, while area multiplies two of them. A card 6 cm by 4 cm is 20 cm around but covers 24 cm². Ask your child to trace the edge with a finger for perimeter, then colour in the inside for area.
How can a teacher bring this geometry practice into class, and is it free?: A teacher pays nothing: pupils open every level in a browser, and nobody registers or installs anything. On squared paper or the board, pupils draw every rectangle with an area of 24 squares. Then they find each perimeter: 1 by 24 gives 50, 2 by 12 gives 28, 3 by 8 gives 22 and 4 by 6 gives 20. For a dashboard of which pupils are improving, add the schools plan, billed per student.

More math to master

Ready to throw down?

Play free ▸