List

Perimeter, Area and Volume (age 11-14)

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.

Blue and White
problem
Favourite

Blue and White

Age
11 to 14
Challenge level
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Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Fence it
problem
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Fence it

Age
11 to 14
Challenge level
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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Isosceles Triangles
problem
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Isosceles Triangles

Age
11 to 14
Challenge level
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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?
Can they be equal?
problem
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Can they be equal?

Age
11 to 14
Challenge level
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Can you find rectangles where the value of the area is the same as the value of the perimeter?
Changing areas, changing perimeters
problem
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Changing areas, changing perimeters

Age
11 to 14
Challenge level
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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?
Perimeter Possibilities
problem
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Perimeter Possibilities

Age
11 to 14
Challenge level
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I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Triangles in a Square
problem
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Triangles in a Square

Age
11 to 14
Challenge level
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What are the possible areas of triangles drawn in a square?
Perimeter Challenge
problem
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Perimeter Challenge

Age
11 to 14
Challenge level
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Can you deduce the perimeters of the shapes from the information given?
Colourful Cube
problem
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Colourful Cube

Age
11 to 14
Challenge level
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A colourful cube is made from little red and yellow cubes. But can you work out how many of each?
Isometric Areas
problem
Favourite

Isometric Areas

Age
11 to 14
Challenge level
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We usually use squares to measure area, but what if we use triangles instead?
An Unusual Shape
problem
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An Unusual Shape

Age
11 to 14
Challenge level
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Can you maximise the area available to a grazing goat?
Shear Magic
problem
Favourite

Shear Magic

Age
11 to 14
Challenge level
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Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
On the Edge
problem
Favourite

On the Edge

Age
11 to 14
Challenge level
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If you move the tiles around, can you make squares with different coloured edges?
Sending a Parcel
problem
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Sending a Parcel

Age
11 to 14
Challenge level
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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
problem
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Cuboid challenge

Age
11 to 16
Challenge level
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What's the largest volume of box you can make from a square of paper?

Changing areas, changing volumes
problem
Favourite

Changing areas, changing volumes

Age
11 to 14
Challenge level
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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?
Triangle in a Trapezium
problem
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Triangle in a Trapezium

Age
11 to 16
Challenge level
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Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
More Isometric Areas
problem
Favourite

More Isometric Areas

Age
11 to 14
Challenge level
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Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
Cuboids
problem
Favourite

Cuboids

Age
11 to 14
Challenge level
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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?
Efficient cutting
problem
Favourite

Efficient cutting

Age
11 to 14
Challenge level
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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
problem
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Cola Can

Age
11 to 14
Challenge level
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An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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
list

Perimeter and Area

Age
11 to 14
Challenge level
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This selection of problems is designed to help you teach Perimeter and Area.
Surface Area and Volume
list

Surface Area and Volume

Age
11 to 14
Challenge level
filled star empty star empty star
This selection of problems is designed to help you teach Surface Area and Volume.




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Perimeter, Area and Volume - Stage 3 STEM footer
 

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.