Quadrilaterals

problem
Favourite

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?
problem
Favourite

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.
problem
Favourite

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?
problem
Favourite

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?
problem

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 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?
problem

Quadrilaterals in a Hexagon

Age

7 to 14

Challenge level

Which of these quadrilaterals can you find in the hexagon?
problem

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?
problem

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.
problem

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?
problem

Folding Flowers 1

Age

7 to 11

Challenge level

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