Question

Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long. 81 108 243

Answer 1

Answer:

Area=$339.2920in^2 \ or \ 108\pi \ in^2$

Step-by-step explanation:

Area of circle is given as:

$A=\pi\ r^2$

Where $r=radius$

To find radius of a circle circumscribing an equilateral triangle, we use the expression

$r=\frac{a\sqrt3}{3}$

Where, a is the length of sides of the equilateral triangle. Therefore:-$r=\frac{18\sqrt3}{3}\\r=6\sqrt3 \ or \ 10.3923in$

We can then proceed and calculate the area of the circle as follows:-

$A=\pi\ r^2\\A=\pi(10.3923)^{2}\\A=339.29\ or \ 108\pi$

*The attached picture illustrates what the circumscribed equilateral triangle looks like