Area of irregular shapes, step by step

Not every shape can be counted in one clean sweep, and that is exactly where organizing a count becomes a skill.

The question

squares

Area of an L-shape by counting

an L, not a rectangle

whole:8 × 6 =48

bite:4 × 1 =4

48 − 4 =44

first way:48 − 4 =44

strip:8 × 5 =40

upright:4 × 1 =4

40 + 4 =44 squares

There is no single row that runs all the way across this one, so counting rows does not work as it stands. Cut it into pieces that ARE rectangles — and there is more than one way.
First way: count the whole rectangle it would be — 8 × 6 = 48 — then take off the bite, 4 × 1 = 4. That leaves 44.
Second way: two rectangles. The strip underneath is 8 × 5 = 40, the part standing on it is 4 × 1 = 4, and 40 + 4 = 44. Two ways agreeing is how you know a count is right.

How it works.

01
There is no single row that runs all the way across this one, so counting rows does not work as it stands. Cut it into pieces that ARE rectangles — and there is more than one way.
02
First way: count the whole rectangle it would be — 8 × 6 = 48 — then take off the bite, 4 × 1 = 4. That leaves 44.
03
Second way: two rectangles. The strip underneath is 8 × 5 = 40, the part standing on it is 4 × 1 = 4, and 40 + 4 = 44. Two ways agreeing is how you know a count is right.