Question

Find the difference in area between the circle and the triangle. Click on the answer until the correct answer is showing.

Possible Answers:
A = 4 pi - 8
A = 9 pi - 9/2 √3
A = 16/3 pi
A = 16
A = 27 pi

Answer 1

A = 9 pi - 9/2 √3

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