There are **51** NRICH Mathematical resources connected to **Quadrilaterals**, you may find related items under Angles, Polygons, and Geometrical Proof.

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Use the information on these cards to draw the shape that is being described.

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The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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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.

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These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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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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Can you find the area of a parallelogram defined by two vectors?

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A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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A game for 2 or more people, based on the traditional card game Rummy.

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This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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How would you move the bands on the pegboard to alter these shapes?

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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.

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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?

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Can you draw a square in which the perimeter is numerically equal to the area?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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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?

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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.

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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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Start with a triangle. Can you cut it up to make a rectangle?

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Can you visualise what shape this piece of paper will make when it is folded?

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Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

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We started drawing some quadrilaterals - can you complete them?

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How many questions do you need to identify my quadrilateral?

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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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A task which depends on members of the group noticing the needs of others and responding.

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Explore the shape of a square after it is transformed by the action of a matrix.

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Investigate 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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I cut this square into two different shapes. What can you say about the relationship between them?

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Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

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How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

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Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

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Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two. . . .

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Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

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ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

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What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

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A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .

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Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

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A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?