Perimeter, Area and Volume - Stage 3

These resources are designed to help students develop useful insights into perimeter, area and volume. For resources about area, perimeter and volume that include shapes and solids with curved edges and surfaces, see our collection Perimeter, Area and Volume - Stage 4.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

Perimeter and Area

This selection of problems is designed to help you teach Perimeter and Area.

Surface Area and Volume

This selection of problems is designed to help you teach Surface Area and Volume.

Perimeter Possibilities

KS 3 Challenge Level:

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

Pick's Theorem

KS 3 Challenge Level:

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.

Painted Cube

KS 3 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Cuboids

KS 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Sending a Parcel

KS 3 Challenge Level:

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Fence It

KS 3 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Isosceles Triangles

KS 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Warmsnug Double Glazing

KS 3 Challenge Level:

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

Can They Be Equal?

KS 3 Challenge Level:

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

Cuboid Challenge

KS 3 Challenge Level:

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

Changing Areas, Changing Perimeters

KS 3 Challenge Level:

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?

Changing Areas, Changing Volumes

KS 4 Challenge Level:

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Area Stage 3 - Short Problems

KS 3 Challenge Level:

A collection of short Stage 3 problems on area and volume.

On the Edge

KS 3 Challenge Level:

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to colour sixteen tiles so that four 4 by 4 squares can be made - one with a green edge, one with a blue edge, one with a yellow edge and one with a red edge.

Triangles in a Square

KS 3 Challenge Level:

What are the possible areas of triangles drawn in a square?

Perimeter Challenge

KS 3 Challenge Level:

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