Resources tagged with: Quadrilaterals

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

Broad Topics > Angles, Polygons, and Geometrical Proof > Quadrilaterals

Shape Draw

Age 7 to 11 Challenge Level:

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

Poly Plug Rectangles

Age 5 to 14 Challenge Level:

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?

Circles in Quadrilaterals

Age 14 to 16 Challenge Level:

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

Overlaps

Age 5 to 7 Challenge Level:

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.

Torn Shapes

Age 7 to 11 Challenge Level:

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

Trapezium Four

Age 14 to 16 Challenge Level:

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

Areas of Parallelograms

Age 14 to 16 Challenge Level:

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

Property Chart

Age 11 to 14 Challenge Level:

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?

Shapely Pairs

Age 11 to 14 Challenge Level:

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...

Quadrilaterals Game

Age 11 to 14 Challenge Level:

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

Stringy Quads

Age 7 to 11 Challenge Level:

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

Transformations on a Pegboard

Age 7 to 11 Challenge Level:

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

A Cartesian Puzzle

Age 7 to 11 Challenge Level:

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

Rectangle Tangle

Age 7 to 11 Challenge Level:

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?

Numerically Equal

Age 7 to 11 Challenge Level:

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

Quadrilaterals

Age 7 to 11 Challenge Level:

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

Quad in Quad

Age 14 to 16 Challenge Level:

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

Flexi Quads

Age 16 to 18 Challenge Level:

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?

Bendy Quad

Age 14 to 16 Challenge Level:

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.

Bracelets

Age 7 to 11 Challenge Level:

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

Triangle Transformation

Age 7 to 14 Challenge Level:

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

Folding Flowers 1

Age 7 to 11 Challenge Level:

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

An Equilateral Triangular Problem

Age 11 to 14 Challenge Level:

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

Completing Quadrilaterals

Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

Guess My Quad

Age 11 to 14 Challenge Level:

How many questions do you need to identify my quadrilateral?

What Am I?

Age 7 to 11 Challenge Level:

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

Opposite Vertices

Age 11 to 14 Challenge Level:

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

Quad Match

Age 7 to 11 Challenge Level:

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

Square Pair

Age 16 to 18 Challenge Level:

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

Bicentric Quadrilaterals

Age 14 to 16 Challenge Level:

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

Cutting it Out

Age 5 to 11 Challenge Level:

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

Rabbit Run

Age 7 to 11 Challenge Level:

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?

Fred the Class Robot

Age 7 to 11 Challenge Level:

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

Flexi Quad Tan

Age 16 to 18 Challenge Level:

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.

Folding

Age 7 to 11 Challenge Level:

What shapes can you make by folding an A4 piece of paper?

The Cyclic Quadrilateral

Age 11 to 16

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.

Making Rectangles, Making Squares

Age 11 to 14 Challenge Level:

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

Cyclic Quad Jigsaw

Age 14 to 16 Challenge Level:

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?

Linkage

Age 11 to 14 Challenge Level:

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?

Arrowhead

Age 14 to 16 Challenge Level:

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?

Hexagon Transformations

Age 7 to 11 Challenge Level:

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

Dividing the Field

Age 14 to 16 Challenge Level:

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. . . .

Strange Rectangle 2

Age 16 to 18 Challenge Level:

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

Strange Rectangle

Age 16 to 18 Challenge Level:

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.

Long Short

Age 14 to 16 Challenge Level:

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

Lawnmower

Age 14 to 16 Challenge Level:

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. . . .

Biggest Bendy

Age 16 to 18 Challenge Level:

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

Set Square

Age 16 to 18 Challenge Level:

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?

Part the Polygons

Age 7 to 11 Short Challenge Level:

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

Is a Square a Rectangle?

Age 7 to 11 Challenge Level:

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