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jollysailorbold
An equilateral triangle is inscribed in a circle with a radius of 6". Find the area of the segment cut off by one side of the triangle.
|dw:1335260036825:dw| it has to be plugged into that.
Hope you can follow my explanation. The inscribed triangle can be cut into 6 equal triangles. One side each of these triangles (the hypotenuse) is equal to the length of the radius. Each triangle is a rt. triangle. Each triangle is a 30 - 60 - 90 triangle. r = 6 So, the sides of the triangle are: Remember for a 30-60-90 triangle: 1 - 2 (hypotenuse) - √3 3 - 6 - 3√3 Area of one triangle: A = (1/2)bh b = 3 h = 3√3 A = (1/2)(3)(3√3) = 9√3/2 6A = 6(9√3/2) = 27√3 Area of circle: A = pi 6^2 A = 36pi Area of segment (there are 3): A = (area of circle - area of triangle)/3 A = (36pi - 27√3)/3 = 12pi - 9√3 = 22.1
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