Perimeter, Area and Volume - Stage 3
Blue and White
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Isosceles Triangles
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
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Triangles in a Square
What are the possible areas of triangles drawn in a square?
Can They Be Equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Perimeter Challenge
Can you deduce the perimeters of the shapes from the information given?
Colourful Cube
A colourful cube is made from little red and yellow cubes. But can you work out how many of each?
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?
Fence It
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Isometric Areas
We usually use squares to measure area, but what if we use triangles instead?
Changing Areas, Changing Volumes
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
Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
Shear Magic
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
On the Edge
If you move the tiles around, can you make squares with different coloured edges?
Sending a Parcel
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
What's the largest volume of box you can make from a square of paper?
Efficient Cutting
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.
Cola Can
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Cuboids
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Perimeter, Area and Volume Short Problems
A collection of short problems on area and volume.
Triangle in a Trapezium
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?