Question

question 4(multiple choice worth 4 points)
(06.01 mc)
a triangle has sides that measure 2 units, 5 units, and 5.39 units. what is the area of a circle with a circumference that equals the perimeter of the triangle? use 3.14 for π, and round your answer to the nearest whole number.
o 39 units²
o 25 units²
o 49 units²
o 12 units²

Explanation:

Step1: Calculate the perimeter of the triangle

The perimeter \(P\) of a triangle with sides \(a = 2\), \(b = 5\), \(c = 5.39\) is \(P=a + b + c\).
\(P=2+5 + 5.39=12.39\) units. This perimeter is equal to the circumference \(C\) of the circle.

Step2: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=12.39\) and \(\pi = 3.14\), we can solve for \(r\).
From \(C = 2\pi r\), we get \(r=\frac{C}{2\pi}\). Substitute \(C = 12.39\) and \(\pi=3.14\) into the formula: \(r=\frac{12.39}{2\times3.14}=\frac{12.39}{6.28}\approx1.97\) units.

Step3: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r\approx1.97\) and \(\pi = 3.14\) into the formula.
\(A=3.14\times(1.97)^{2}=3.14\times3.8809\approx12\) units².

Answer:

12 units²