Question

When NB = 12 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.

Answer 1

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Given: NB = 12 ft, Angle-120°
Asked: area of the region that is not shaded.
Substitute the given values in the equation in finding the area of a circle.
A = πr² 
A = ⅔π(12 ft)² 
A = 96π ft² 
(Since 120° is 1/3 of the circle. it is then understood that the unshaded parts must be 2/3 of the circle.)
Since you already have the area, find the area of the triangle to add it to the area of the circle to find the area of the unshaded part. By using a handy trigonometry, you can tell that their will be 2 triangles of 12 ft (if you are going to divide 120° angle). From this, you'll see that there will be one of the smaller triangles having a  the height of 6 ft and the base is 6√3 ft. Substitute the values.
A = ½bh 
A = ½(6 ft)(6√3 ft) * 2 
A = 36√3 ft² 

Add them up and you will have the exact answer  96π + 36√3 ft², when rounded to the nearest tenth, you will have  364 ft².