These are rectangles, so the area of this shape is a sum of areas:
- blue: a = x, b = x, so area: x · x = x²
- pink: a = 6, b = x, so area: 6 · x = 6x
- green: a = 5, b = x, so 5 · x = 5x
- orange: a = 6, b = 5, so 6 · 5 = 30
The area of the entire rectangle is: x² + 6x + 5x + 30 = x² + 11x + 30
We can also count this area by multiplication of side lengths of big rectangle:
a = x + 6, b = x + 5
then the area is:
(x + 6)(x + 5) = x · x + x · 5 + 6 · x + 6 · 5 = x² + 5x + 6x + 30 =
= x² + 11x + 30
