Quadrilaterals

There are 65 NRICH Mathematical resources connected to Quadrilaterals
Rectangle Tangle
problem
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Rectangle tangle

Age
7 to 11
Challenge level
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The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

Torn Shapes
problem
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Torn shapes

Age
7 to 11
Challenge level
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These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Bendy Quad
problem
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Bendy quad

Age
14 to 16
Challenge level
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Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
A Cartesian Puzzle
problem
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A cartesian puzzle

Age
7 to 11
Challenge level
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Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Overlaps
problem
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Overlaps

Age
5 to 7
Challenge level
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What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

Transformations on a Pegboard
problem
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Transformations on a pegboard

Age
7 to 11
Challenge level
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How would you move the bands on the pegboard to alter these shapes?
circles in quadrilaterals
problem
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Circles in quadrilaterals

Age
14 to 16
Challenge level
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Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Square split into a triangle and trapezium
problem
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Tangram tangle

Age
5 to 7
Challenge level
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If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Flexi Quads
problem
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Flexi quads

Age
16 to 18
Challenge level
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A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?
Square It
problem
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Square it

Age
11 to 16
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.