Question

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. 12 units² 49 units² 25 units² 39 units²

Explanation:

Step1: Calculate the perimeter of the triangle

The perimeter $P$ of a triangle with side - lengths $a = 2$, $b = 5$, and $c = 5.39$ is $P=a + b + c$.
$P=2 + 5+5.39=12.39$ units.

Step2: Find the radius of the circle

The formula for the circumference of a circle is $C = 2\pi r$. Since $C = P=12.39$ and $\pi = 3.14$, we can solve for $r$.
$r=\frac{C}{2\pi}=\frac{12.39}{2\times3.14}=\frac{12.39}{6.28}\approx1.97$ 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.
$A = 3.14\times(1.97)^{2}=3.14\times3.8809\approx12$ square units.

Answer:

12 units²