Question

Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)

I need this in pi form.

Answer 1

A square inscribed in a circle.
s = 6
r = (1/2) (diagonal of square)
diagonal of square = hypotenuse of isosceles triangle with equal sides of length 6.
6^2 + 6^2 = h^2
36 + 36 = h^2
72 = h^2
h = 6√2
r = (1/2)h
r = (1/2)(6√2)
r = 3√2
Area of circle:
A = pi r^2
A = pi(3√2)^2
A = 18pi
Area of square:
A = s^2
A = 6^2
A = 36
There are four segments formed by the square and circle.
Area of a segment:
(area of circle - area of square)/4
(18pi - 36)/4 = (9pi - 18)/2 = (9/2)pi - 9 = 5.1 in^2

Answer 2

Thanks!

Answer 3

np:)