Area - triangles, quadrilaterals, compound shapes

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

Can you find the area of a parallelogram defined by two vectors?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?