Question

On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (0, -2√) and (2√, 0). What is the area of the region, rounded to the nearest tenth, that is inside the square but outside the circle?

Answer 1

0.9 square units

Explanation:

We assume you intend the vertices of the square to be (±√2, 0) and (0, ±√2). Then the diagonals of the square are 2√2 in length and its area is ...

(1/2)(2√2)² = 4

The radius of the inscribed circle is 1, so its area is ...

π·1² = π

and the area outside the circle, but inside the square is the difference of these areas:

area of interest = 4 - π ≈ 0.858407

area of interest ≈ 0.9