Area - triangles, quadrilaterals, compound shapes

problem
Triangle in a trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
problem
The farmers' field boundary

Age

11 to 14

Challenge level

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

Age

7 to 11

This task challenges you to create symmetrical U shapes out of rods and find their areas.
problem
Triangle transformation

Age

7 to 14

Challenge level

Start with a triangle. Can you cut it up to make a rectangle?
problem
Completing quadrilaterals

Age

11 to 14

Challenge level

We started drawing some quadrilaterals - can you complete them?
problem
Towering trapeziums

Age

14 to 16

Challenge level

Can you find the areas of the trapezia in this sequence?
problem
Quadrilaterals in a square

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 18

Challenge level

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

Age

11 to 14

Challenge level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?