Question

A square has been circumscribed inside of a

circle as shown to the right. If the area of the
circles is 16 units, determine the area of the
square.

Answer 1

Area of Square ≈ 10.17

Explanation:

It would be difficult to derive this answer in terms of π, so let us assume π to be 3.14 units;

Now given the area of this circle we can derive the radius through a simple " Area of Circle " formula πr^2 where r ⇒ radius;

Area of Circle ⇒ πr^2,

16 units^2 = πr^2,

16 = 3.14 * r^2,

5.09554140127... = r^2,

r = 2.25733059193, r ≈ 2.255,

diameter ⇒ ≈ 4.51

The diameter splits the square into two right triangles, such that Pythagorean Theorem can be applied. We don't know the length of either one of the legs to solve this, but as in a square all sides are ≅, we can say;

4.51^2 = x^2 + x^2 ⇒ x is one of the legs of the right triangles,

2x^2 = 4.51^2,

2x^2 = 20.3401,

x^2 = 10.17005,

x ≈ 3.19

Thus, the area of this Square is ≈ 3.19 * 3.19 ⇒ 10.17005;

Area of Square ≈ 10.17