Final answer:
The formula for the area of a semicircle is A = (πr²)/2, derived by dividing the area of a full circle, which is πr², by 2 since a semicircle is half of a circle.
Step-by-step explanation:
The formula for the area of a semicircle can be derived from the formula for the area of a full circle. A semicircle is half of a circle, so to find its area, you divide the area of a full circle by 2. The area of a full circle is given by A = πr², where π is approximately 3.14159 and r is the radius. Therefore, the area of a semicircle is A = (πr²)/2. If you have the diameter instead, remember that the diameter is twice the radius (d = 2r), so the area can also be expressed as A = (π(d/2)²)/2.