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This selection of problems is a great starting point for learning about Perimeter and Area.

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This selection of problems is a great starting point for learning about Surface Area and Volume

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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?

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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?

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

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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?

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

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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.

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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?

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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?

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

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What's the largest volume of box you can make from a square of paper?

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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?

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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?

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

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

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

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

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

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

A collection of short problems on area and volume.

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Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

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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?