Squares all around

Why not prove it with a gif?

Let $A$ be the total area.

fibonacci $\implies A = 8 \times (8+5)=\boxed{104}$

Fibonacci squares comes to mind.

Denoting the length of green squares as $F_1, F_2$ , the brown square: $F_3$ , blue square: $F_4$ , purple square: $F_5$ , red square: $F_6$ . So the answer is simply $(F_6 + F_5 ) \times ( F_5 + F_4 ) = F_7 \times F_6 = 13 \times 8 = \boxed{104}$ .

The generalization is: for a total of $n$ squares used in the Fibonacci squares, the area is $F_{n+1} F_n$ (thus proving the identity $\displaystyle \sum_{k=1}^n F_k ^2 = F_{n+1} F_n$ geometrically).

Use Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8

We want to find the area of the entire rectangle.

Side of Red Square X (Side of Red Square + Side of Purple Square)

We know that the green squares are each 1 and that the orange square must have a side length of 2.

Then, the Blue must have Green + Orange, or 3.

Purple is 2Green + Blue = 5

Red is Orange + Green + Purple = 8

So going back to our first equation,

WE replace into this Side of Red Square X (Side of Red Square + Side of Purple Square)

To get: 8 X (8+5) = 8 X 13 = 104

I calculated mentally.

This is a piece of ice cream. Just draw a diagram and label the sides correctly. Drawing the correct diagram is half of the solution.

Fibonacci explained :). Answer is 104

Green 1, orange2, blue3, purple5, red8 so 8*13=104