There are **52** NRICH Mathematical resources connected to **Quadrilaterals**, you may find related items under Angles, Polygons, and Geometrical Proof.

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 ten numbered shapes?

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

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?

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

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.

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

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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

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?

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...

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

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

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

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

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?

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

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

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

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?

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.

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

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

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

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

We started drawing some quadrilaterals - can you complete them?

How many questions do you need to identify my quadrilateral?

Can you draw the shape that is being described by these cards?

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

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

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

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

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

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?

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

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.

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

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?

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?

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?

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

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. . . .

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

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.

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

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. . . .

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

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?

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