Quadrilaterals

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?

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.

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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

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

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

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?

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

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