SOLUTION: How do you find the shaded are of a quadrilateral if the quadrilateral is a square and all arcs are arcs of a circle of radius 6 cm and there are four arcs one for each corner? Tha

Algebra ->  Surface-area -> SOLUTION: How do you find the shaded are of a quadrilateral if the quadrilateral is a square and all arcs are arcs of a circle of radius 6 cm and there are four arcs one for each corner? Tha      Log On


   

Question 599110: How do you find the shaded are of a quadrilateral if the quadrilateral is a square and all arcs are arcs of a circle of radius 6 cm and there are four arcs one for each corner? Thanks for helping :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This square is inscribed in the circle of radius 6. So the diagonal of the square is 2*6 = 12 cm


Let x = length of the side of the square


So by the pythagorean theorem

a^2 + b^2 = c^2

x^2 + x^2 = 12^2

2x^2 = 144

x^2 = 144/2

x^2 = 72

x = sqrt(72)

x = 6*sqrt(2)


So the length of the side of the square is 6*sqrt(2) cm


Now use it in the area for a square formula

A = s^2

A = (6*sqrt(2))^2

A = (6*6)*(sqrt(2)*sqrt(2))

A = 36*sqrt(4)

A = 36*2

A = 72

So the area of the square is 72 square cm.