
Area - triangles, quadrilaterals, compound shapes
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problemInvestigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
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problem
Maths filler 2
Can you draw the height-time chart as this complicated vessel fills with water? -
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Gutter
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
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problem
Twice as big?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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Trapezium four
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
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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?
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Uncanny triangles
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas? -
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Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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Shear magic
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?