Skip to main content
MathidiaMathematics Academy
Quadratic expressions
Lesson 20 of 75
Review

Quadratic area models

Objective. Build quadratic expressions from geometric contexts.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Quadratic area models build an algebraic quadratic expression from a geometric diagram, usually by splitting a shape into rectangles whose areas are added together. A common approach is to draw a large rectangle with sides written as binomials, such as (x + 3) by (x + 5), and recognise that its total area equals the expansion of those brackets, x² + 8x + 15. Each smaller rectangle inside the diagram represents one term of the expansion: an x² square, two rectangles of area 3x and 5x, and a small 3 by 5 rectangle of area 15. This visual method helps explain why the expanded quadratic has exactly those four terms before simplifying.

Worked example

A rectangular garden has sides (x + 4) m and (x + 2) m. Find a quadratic expression for its area using an area model.

Diagram of a rectangle
  1. 1Split the rectangle into four regions: x², 2x, 4x and 4×2.
  2. 2The x² region comes from x × x.
  3. 3The two cross-term regions give 2x and 4x, totalling 6x.
  4. 4The constant region is 4 × 2 = 8, so the total area is x² + 6x + 8.

Answer: x² + 6x + 8 m²

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils sometimes add only the areas of two rectangles instead of all four regions in the grid, missing the cross terms and producing an incomplete expression like x² + 15. Always include all four regions: the x² square, both cross-term rectangles, and the constant rectangle.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard