To figure the area of a circle with a diameter of 12 inches, which formula would you use?

To figure the area of a circle with a diameter of 12 inches, which formula would you use?

• A. A = (3.14 x 12 inches x 12 inches) ÷ 4
• B. A = πr^2
• C. A = πd^2 ÷ 2
• D. A = 2πr

Answer: (A)

When you know the diameter, you can find the area without converting to radius by using A = π d^2 / 4. This comes from substituting r = d/2 into A = π r^2, giving A = π (d/2)^2 = π d^2 / 4. For a diameter of 12 inches: A = π × 12^2 / 4 = π × 144 / 4 = π × 36 ≈ 113.04 square inches (using π ≈ 3.14). So the best choice is the one that uses A = π d^2 ÷ 4. The other options don't fit: using A = π r^2 requires the radius, not the diameter; A = π d^2 ÷ 2 would overcount the area; and A = 2πr gives the circumference, not the area.

When you know the diameter, you can find the area without converting to radius by using A = π d^2 / 4. This comes from substituting r = d/2 into A = π r^2, giving A = π (d/2)^2 = π d^2 / 4.

For a diameter of 12 inches: A = π × 12^2 / 4 = π × 144 / 4 = π × 36 ≈ 113.04 square inches (using π ≈ 3.14). So the best choice is the one that uses A = π d^2 ÷ 4.

The other options don't fit: using A = π r^2 requires the radius, not the diameter; A = π d^2 ÷ 2 would overcount the area; and A = 2πr gives the circumference, not the area.