Students learn how to form and solve quadratic equations from geometry problems. Problems include finding the area of a rectangle with algebraic lengths to setting up an equation from similar shapes.

The start of the lesson recaps finding the area of composite shapes with algebraic lengths as this is needed throughout the lesson. The plenary challenges students to derive and solve a quadratic equation from the surface area of a cuboid.

**Differentiated Learning Objectives**

- All students should be able to form a quadratic equation from a rectilinear area.
- Most students should be able to use geometrical facts to set up and solve a quadratic equation when a = 1.
- Some students should be able to form and solve a quadratic equation from geometrical facts.