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There are **34** NRICH Mathematical resources connected to **Perimeter**, you may find related items under Measuring and calculating with units.

Problem
Primary curriculum
Secondary curriculum
### Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perimeter Challenge

Can you deduce the perimeters of the shapes from the information given?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Draw

Use the information on these cards to draw the shape that is being described.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Through the Window

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Age 7 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Dicey Perimeter, Dicey Area

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perimeter Possibilities

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Changing Areas, Changing Perimeters

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perimeter Expressions

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Area and Perimeter

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Can They Be Equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sizing Them Up

Can you put these shapes in order of size? Start with the smallest.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Warmsnug Double Glazing

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### On the Edge

If you move the tiles around, can you make squares with different coloured edges?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapes on the Playground

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Numerically Equal

Can you draw a square in which the perimeter is numerically equal to the area?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rod Area

This task challenges you to create symmetrical U shapes out of rods and find their areas.

Age 7 to 11

List
Primary curriculum
Secondary curriculum
### Being Resilient - Primary Measures

Measure problems at primary level that may require resilience.

Age 5 to 11

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Resourceful - Primary Measures

Measure problems at primary level that require careful consideration.

Age 5 to 11

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Collaborative - Primary Measures

Measure problems for primary learners to work on with others.

Age 5 to 11

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Curious - Primary Measures

Measure problems for inquiring primary learners.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cutting it Out

I cut this square into two different shapes. What can you say about the relationship between them?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Von Koch Curve

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squareflake

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Smaller and Smaller

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Circuits, Seven Spins

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coins on a Plate

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lawn Border

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fencing Lambs

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

Age 7 to 11

Challenge Level