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
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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) (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.
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