Question 952115: PLEASE HELP!
An equilateral triangle is inscribed in a circle with a radius of 6 ft. Find the area of the shaded region shown. Give the exact answer. (Do not approximate
π or any square root.)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Where is the shaded region?
****************
student answer
Its a circle with a triangle in the middle. The shaded region is the area around the triangle
***************
The area of the circle = pi*r^2 = pi*6^2 = 36*pi
The side(s) of the equilateral triangle is calculated
s = square root(3)*r, where r is the radius of the circle
s = 6*square root(3)
**************
The height(h) of the equilateral triangle is calculated using the pythagorean theorem,
ap^2 + (3*square root(3))^2 = 6^2, where ap is the apothem of the equilateral triangle
ap^2 = 36 - 27 = 9
ap = 3
h = 6 + 3 = 9
**************
area of triangle = (1/2) * (6*square root(3)) * 9
area of triangle = 27*square root(3)
**************
area of shaded area = (36*pi) - (27*square root(3) )
|
|
|
