There are 22 results
Broad Topics > Angles, Polygons, and Geometrical Proof > Quadrilaterals
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.
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.
Quad in Quad
Age 14 to 18
Challenge Level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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.
Triangle Transformation
Age 7 to 14
Challenge Level
Start with a triangle. Can you cut it up to make a rectangle?
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?
Opposite Vertices
Age 11 to 14
Challenge Level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
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.
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?
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. . . .
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. . . .
NRICH is part of the family of activities in the Millennium Mathematics Project.