Question

a triangle has sides that measure 4 units, 6 units, and 7.25 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.
17 units²
24 units²
54 units²
94 units²

Explanation:

Step1: Calculate triangle perimeter

$4 + 6+7.25=17.25$ units. This is the circumference $C$ of the circle.

Step2: Find radius of circle

We know $C = 2\pi r$. So, $r=\frac{C}{2\pi}$. Substituting $C = 17.25$ and $\pi=3.14$, we get $r=\frac{17.25}{2\times3.14}\approx2.75$ units.

Step3: Calculate area of circle

The area formula is $A=\pi r^{2}$. Substituting $r\approx2.75$ and $\pi = 3.14$, we have $A=3.14\times(2.75)^{2}=3.14\times7.5625\approx24$ square - units.

Answer:

24 units²