The image below is a triangle drawn inside a circle with center o:
8 inches
5 inches
4 inches
which of the following expressions shows the area, in square inches, of the circle?
(tt = 3.14)
3.14.42
3.14 . 52
3.14.5
3.14 22

  area ≈ 24π

Step-by-step explanation:

We have solved this problem two ways:

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Drawing

A drawing of the figure (below) can help you find the radius of circle O. It is about 4.89 inches, so the area of circle O is about ...

  area = πr^2 = π(4.89 in)^2 ≈ 23.9π ≈ 24π . . . .square inches

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Formulas

There is an interesting relationship between the area of the triangle and the radius of the circumscribing circle:

  r = (abc)/(4A) . . . . . where a, b, c are the triangle side lengths, and A is the triangle area

Heron's formula can tell us the area of the triangle from the side lengths:

  A = √(s(s-a)(s-b)(s-c)) . . . . where s = (a+b+c)/2

For the given triangle with side lengths 4, 5, and 8 (inches), the area can be found as ...

  s = (4+5+8)/2 = 8.5

  A = √(8.5·4.5·3.5·0.5) = √66.9375 ≈ 8.1815 . . . square inches

Then the radius of the circle is ...

  r = (4·5·8)/(4·8.1815) = 4.889 . . . inches

The area of the circle is then ...

  Circle O area = πr^2 = π(4.889 in)^2 = 23.9π in^2

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The closest answer choice is 3.14×22.