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Find the area of the shaded portion. Show all work for full credit. Download gif

Carlton Burgess

in Mathematics

1 answer

1 answer

Jennifer Patterson on July 15, 2018

So.. if you realize, the central angle for the shaded part, is 120°, therefore, by the "tangent segment" theorem, the two tangents are the same length, if we have to run a bisector of an angle of 120, splitting it into two 60 and 60 angles, we're going to cut the angle out of the circle, where the tangents meet in halfnotice the image below, you can end up with two 30-60-90 triangles, to get the sides, you can use the 30-60-90 rule, in the image, in which case, notice, x = 6the shaded area is, the entire area of the two triangles, the less the circle of the sector with the 120° angleso.. just get the area of each triangle is 1/2 bh, add them up, THEN get the area of the circle sector, and subtract from the angle of the sumwhat that you have left, is the shaded area, the remaining part of the triangle the sum, that was not subtractedand surely you know

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