Area of composite figures, step by step

A composite figure has no formula of its own, and that is the point.

The question
1271961319 cm²

Area of a 19 by 19 L-shape

19 cm19
  1. First way: pretend the bite was never taken. The whole rectangle would be 19 × 19 = 361.
  2. Then take the bite off. It is 7 × 6 = 42, so the L is 361 − 42 = 319 square cm.
  3. Second way, and it works on any of these: cut the L into two rectangles.
  4. The bottom strip is 19 × 13 = 247, and the piece standing on it is 12 × 6 = 72.
  5. 247 + 72 = 319 square cm — the same answer as the first way. Two methods that agree is how you know the answer is right.

How it works.

  1. 01

    First way: pretend the bite was never taken. The whole rectangle would be 19 × 19 = 361.

  2. 02

    Then take the bite off. It is 7 × 6 = 42, so the L is 361 − 42 = 319 square cm.

  3. 03

    Second way, and it works on any of these: cut the L into two rectangles.

  4. 04

    The bottom strip is 19 × 13 = 247, and the piece standing on it is 12 × 6 = 72.

  5. 05

    247 + 72 = 319 square cm — the same answer as the first way. Two methods that agree is how you know the answer is right.