What is the formula for finding the area of a semicircle?

What is the formula for finding the area of a semicircle?

• A. A=πr²
• B. A=1/2 * π * r²
• C. A=2πr
• D. A=πr

Answer: (B)

The formula for finding the area of a semicircle is derived from the area of a full circle. The area \( A \) of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle. Since a semicircle is half of a full circle, to find the area of a semicircle, you would take half of the area of the full circle. This leads to the formula: \[ A = \frac{1}{2} \times \pi r^2 \] This equation clearly shows that to obtain the area of a semicircle, you multiply the area of a full circle by \( \frac{1}{2} \). Thus, the correct answer reflects the appropriate adjustment for the semicircle, accurately representing its area. The other choices do not apply to the area of a semicircle: the first choice is the area of a full circle, the third choice represents the circumference, and the fourth choice does not correspond to either area or circumference, hence they cannot be used to describe the area of a semicircle.

The formula for finding the area of a semicircle is derived from the area of a full circle. The area ( A ) of a full circle is given by the formula ( A = \pi r^2 ), where ( r ) is the radius of the circle.

Since a semicircle is half of a full circle, to find the area of a semicircle, you would take half of the area of the full circle. This leads to the formula:

[

A = \frac{1}{2} \times \pi r^2

]

This equation clearly shows that to obtain the area of a semicircle, you multiply the area of a full circle by ( \frac{1}{2} ). Thus, the correct answer reflects the appropriate adjustment for the semicircle, accurately representing its area.

The other choices do not apply to the area of a semicircle: the first choice is the area of a full circle, the third choice represents the circumference, and the fourth choice does not correspond to either area or circumference, hence they cannot be used to describe the area of a semicircle.