Answer:
A = 9 pi - 9/2 √3
Step-by-step explanation:
Both the triangle area and the circle area are irrational, so the only sensible answer choice is the 2nd one. (The triangle area is irrational because it involves the √3; the circle area is irrational because it involves π.)
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The triangle area is given by ...
A = 1/2·b·h
The short leg of the triangle is 3, so the height from the diameter is
h = 3·sin(60°) = 3(√3)/2
so the triangle area is ...
A = (1/2)(6)(3√3)/2 = (9/2)√3
This should be enough to make an appropriate answer selection.
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The circle area is given by ...
A = πr² = π·3² = 9π
This, too, should be enough to make an appropriate answer selection.
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Then the shaded difference between the circle area and the triangle area is ...
circle area - triangle area
= 9π - (9/2)√3
