Hi ALL,
We're told that the circle above has center A and its area is 144pi. We're asked for the perimeter of sector ABCD. This question is based on several Geometry formulas - and we're given all of the necessary numbers to work with - so we just have to work through the appropriate math to answer it.
To start, ABCD is composed of 2 radii and a section of the circumference. That arc is based on a 45-degree angle, so it is 45/360 = 1/8 of the total circumference.
With an area of 144pi, we can solve for the radius:
Area = (pi)(R^2) = 144pi
R^2 = 144
R = 12
With a radius of 12, the total circumference is (2)(pi)(R) = (2)(pi)(12) = 24pi. The arc of ABCD is (1/8)(24pi) = 3pi
Thus, the total perimeter of ABCD is 12+12+3pi = 24 + 3pi
Final Answer:
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