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There are **58** NRICH Mathematical resources connected to **Quadrilaterals**, you may find related items under Angles, polygons, and geometrical proof.

Problem
Primary curriculum
Secondary curriculum
### Seeing Parallelograms

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 parallelogram.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rhombus It

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 rhombus.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parallelogram It

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 parallelogram.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Seeing Squares

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.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Equilateral Triangular Problem

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Completing Quadrilaterals

We started drawing some quadrilaterals - can you complete them?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guess my Quad

How many questions do you need to identify my quadrilateral?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Draw

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Poly Plug Rectangles

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Opposite Vertices

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quad Match

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Circles in Quadrilaterals

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Overlaps

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.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Torn Shapes

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Areas of Parallelograms

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Property Chart

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapely Pairs

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...

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Quadrilaterals Game

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stringy Quads

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square It

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformations on a Pegboard

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Cartesian Puzzle

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rectangle Tangle

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Numerically Equal

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadrilaterals

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quad in Quad

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flexi Quads

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bendy Quad

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bracelets

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rabbit Run

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fred the Class Robot

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flexi Quad Tan

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.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### The Cyclic Quadrilateral

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.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Making Rectangles, Making Squares

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cyclic Quad Jigsaw

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Linkage

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arrowhead

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hexagon Transformations

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dividing the Field

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 trapeziums each of equal area. How could he do this?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Strange Rectangle 2

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Strange Rectangle

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Long Short

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lawnmower

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 grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Biggest Bendy

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Set Square

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Part the Polygons

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Is a Square a Rectangle?

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut and Make

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Age 7 to 11

Challenge Level