To solve the problem of finding the area of the circle with a diameter of 12, we use the formula for the area of a circle:

$A = \pi r^2$

Where:

• $r$ is the radius of the circle, and
• $A$ is the area.

Step-by-step solution:

1. The diameter is given as 12, so the radius $r$ is half of the diameter: $r = \frac{12}{2} = 6$

2. Plug the radius into the formula for the area: $A = \pi (6)^2 = \pi \times 36$

3. Therefore, the area of the circle is: $A = 36\pi$

The correct answer is 36π.

Would you like any more details, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you find the circumference of a circle if the diameter is known?
2. If the diameter were doubled, how would the area of the circle change?
3. What is the relationship between the radius and the diameter of any circle?
4. How would you express the area of a circle in terms of its diameter instead of its radius?
5. What is the area of a semicircle with the same diameter of 12?

Tip: Always remember that the radius is half the diameter when working with circles!