Quadrilaterals

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

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?

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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.

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

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

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

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