Area - triangles, quadrilaterals, compound shapes

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

Can you draw the height-time chart as this complicated vessel fills with water?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?