Question 599560
What is the area of one segment formed by a square with sides of 6 inches inscribed in a circle.
Draw this out and you can see the hypotenuse of the square is also the diameter of the circle, therefore
radius = {{{sqrt(6^2+6^2)/2}}} = {{{sqrt(72)/2}}}= {{{sqrt(36*2)/2}}} ={{{(6*sqrt(2))/2}}} = {{{3*sqrt(2)}}}
Find the area of the circle
A = {{{pi*(3*sqrt(2))^2}}}
A = {{{pi*(9*2)}}}
A = {{{pi*18}}}
A = 56.55 sq/inches
Subtract the area of the square
56.55 - 36 = 20.55
Find the area of one of the 4 segments
{{{20.55/4}}} = 5.14 sq/in in one segment