Area - triangles, quadrilaterals, compound shapes

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

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

What's special about the area of quadrilaterals drawn in a square?

What are the possible areas of triangles drawn in a square?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

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

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?