Question

$\pi r^2$ (the symbol is pi) is the formula to find the area of a ______
select one:
a. triangle
b. circle
c. square
d. hexagon

the side of an equilateral triangle is 12. its area is
select one:
a. $36 \sqrt{3}$
b. 48
c. 144
d. 72

Explanation:

Step1: Identify circle area formula

The given formula $\pi r^2$ (written as $\Pi r2$ in the question) is the standard formula for the area of a circle, where $r$ is the radius.

Step2: Recall equilateral triangle area formula

The formula for the area of an equilateral triangle with side length $s$ is $\frac{\sqrt{3}}{4}s^2$.

Step3: Substitute $s=12$ into the formula

$$\text{Area} = \frac{\sqrt{3}}{4} \times 12^2$$
$$= \frac{\sqrt{3}}{4} \times 144$$
$$= 36\sqrt{3}$$

Answer:

1. b. circle
2. a. $36 \sqrt{3}$