Perimeter, Area and Volume - Stage 3

Perimeter Possibilities

KS 3 Challenge Level:

Challenge Level:1

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

Pick's Theorem

KS 3 Challenge Level:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:1

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:

Challenge Level:1

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:

Challenge Level:1

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

On the Edge

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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.