Question

Find the exact value of the area

of the shaded region. The length
of the side of the grid squares
is I unit.

Answer 1

26π square units

Explanation:

You want the shaded area of the figure shown.

Quarter circle

Each quarter-circle has an area of ...

A = 1/4πr²

There are quarter-circles with radii 1, 1, 2, 3, 5, and 8 units.

The area is π/4 times the sum of the squares of these values:

(π/4)(1² +1² +2² +3² +5² +8²) = 26π

The area of this portion of a Fibonacci spiral is 26π square units.

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