Students learn how to use Pythagoras' Theorem to calculate unknown lengths in a range of problems involving right-angled triangles. As learning progresses this is linked to finding the area and perimeter of composite shapes.

At the start of the lesson students find the perimeter of a quadrilateral plotted on Cartesian axes by calculating the hypotenuse length between the vertices. In the plenary they are challenged to calculate the perpendicular height of a triangle whose vertices form the center of three identical circles.

**Differentiated Learning Objectives**

- All students should be able to calculate the length between two coordinate pairs.
- Most students should be able to use Pythagoras’ Theorem to solve problems involving right-angled triangles.
- Some students should be able to calculate the longest diagonal in a cuboid.