Quadrilaterals

problem

Square Bisection

Age

11 to 14

Challenge level

Weekly Problem 8 - 2008
In how many ways can a square be cut in half using a single straight line cut?
problem

Outside the Nonagon

Age

11 to 14

Challenge level

Weekly Problem 44 - 2010
Extend two of the sides of a nonagon to form an angle. How large is this acute angle?
problem

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?
problem

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?
problem

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

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?
problem

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?
problem

Unusual Quadrilateral

Age

14 to 16

Challenge level

This quadrilateral has an unusual shape. Are you able to find its area?
problem

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?
problem

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.