Question

a triangle has sides that measure 4 units, 6 units, and 7.21 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

First, find the perimeter of the triangle. The sides of the triangle are 4 units, 6 units, and 7.21 units. The perimeter $P$ of a triangle is the sum of its side - lengths. So $P=4 + 6+7.21=17.21$ units.

Step2: Find the radius of the circle

The circumference $C$ of the circle is equal to the perimeter of the triangle, so $C = 17.21$ units. The formula for the circumference of a circle is $C = 2\pi r$. We know that $C=17.21$ and $\pi = 3.14$. Then $r=\frac{C}{2\pi}=\frac{17.21}{2\times3.14}=\frac{17.21}{6.28}\approx2.74$ units.

Step3: Calculate the area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r\approx2.74$ and $\pi = 3.14$ into the formula. $A = 3.14\times(2.74)^{2}=3.14\times7.5076\approx23.57\approx24$ square units.

Answer:

24 units²