Area by Decomposition

Free interactive math game: Area by Decomposition — L-shape area. Part of the Geometric Shapes category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. Find the total area of the L-shape by decomposing it.

About this exercise

Breaking an awkward shape into pieces whose areas you can name.

How to solve it

Draw one or two cuts that turn the figure into rectangles, work out each piece from its own sides, and add the pieces up. Where the figure is nearly a full rectangle, taking the big rectangle and subtracting the notch is often faster.

Worked example

An L-shape cut once becomes two rectangles, say 4 x 3 and 6 x 2, so the total is 12 + 12 = 24.

Common mistake

Reusing a side length that the cut has shortened. After cutting, each piece has its own measurements, and some differ from the labels on the outline.