Perimeter, Area and Volume - Stage 3

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

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.

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?

Isometric Areas

KS 3 Challenge Level:

We usually use squares to measure area, but what if we use triangles instead?

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?

Perimeter Possibilities

KS 3 Challenge Level:

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

Triangles in a Square

KS 3 Challenge Level:

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

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?

Perimeter Challenge

KS 3 Challenge Level:

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

Blue and White

KS 3 Challenge Level:

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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?

Colourful Cube

KS 3 Challenge Level:

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

An Unusual Shape

KS 3 Challenge Level:

Can you maximise the area available to a grazing goat?

Changing Areas, Changing Volumes

KS 3 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?

More Isometric Areas

KS 3 Challenge Level:

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

On the Edge

KS 3 Challenge Level:

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

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?

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?

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.

Efficient Cutting

KS 3 Challenge Level:

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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?

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?

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?

Cola Can

KS 3 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Perimeter, Area and Volume Stage 3 - Short Problems

KS 3

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