Area of Circles and Semicircles
Ever wondered how much space a circle takes up? The area of a circle equals π × r². For example, with a circle of radius 2.9 ft, we calculate π × 2.9² ≈ 26.42 square feet. When you have the diameter instead (like 35 mm), simply divide by 2 first to get the radius (17.5 mm).
Semicircles are just half of a circle, so their area is (π × r²) ÷ 2. For a semicircle with radius 9.4 inches, we get (π × 9.4²) ÷ 2 ≈ 138.80 square inches. For a semicircle with radius 22 inches, the area is about 760.27 square inches.
Sometimes you'll need to work backward. If you know the area of a circle is 490.87 square feet, you can find the radius by using r = √(A ÷ π). This gives a radius of 12.5 feet, making the diameter 25 feet. Similarly, for a semicircle with area 76.97 km², you'd use r = √(2A ÷ π) to get approximately 7 km.
Pro Tip: Always check if you're working with the radius or diameter! Mixing these up is a common mistake that leads to answers that are off by a factor of 2 or 4.
When finding the area of a sector (a "pizza slice" of a circle), use the formula (θ ÷ 360°) × π × r², where θ is the central angle. For example, a sector with radius 11 inches and angle 64° has an area of (64 ÷ 360) × π × 11² ≈ 67.58 square inches.
