Quadrilaterals

Which of these quadrilaterals can you find in the hexagon?

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

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

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.

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?

I cut this square into two different shapes. What can you say about the relationship between them?

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.