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?
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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

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.
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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.
problem

Stellar Angles

Age

11 to 14

Challenge level

Weekly Problem 30 - 2013
What is the angle $x$ in the star shape shown?
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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?