Ready to master areas of circles and sectors? This guide...
Geometry514 views·Updated Jul 24, 2026·2 pagesExploring Areas of Circles and Circular Sectors
Josephine McCotter@jp.mccotter
1
of 2
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.
2
of 2
Area of Circle Sectors
Sectors are like pizza slices cut from a circle. To find their area, you need to know the central angle (θ) and radius . The formula is (θ ÷ 360°) × π × r², which gives you the fraction of the circle's area based on the angle.
When working with sectors, you'll often need to do some angle calculations first. For example, if a circle shows angles of 136° + 136° = 272°, then your sector takes up (272 ÷ 360) × π × 9² ≈ 192.27 square centimeters. For trickier problems, subtract known angles from 360° to find the sector angle.
Some problems may require you to identify the radius correctly. In problem #13, BD is the diameter (18 cm), so the radius is 9 cm. In problem #16, SR represents the diameter (26 m), making the radius 13 m. Always check whether you're given the radius or diameter!
Remember: When calculating sector areas, the angle must be expressed as a fraction of the full circle (360°). So a 90° angle represents 1/4 of the circle's area.
Sometimes you'll need to piece together angles from multiple sections. In problem #14, you need to add angles , then subtract from 360° to get 144° for the desired sector. Using (144 ÷ 360) × π × 5.3² gives approximately 35.30 square kilometers.
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Geometry514 views·Updated Jul 24, 2026·2 pagesExploring Areas of Circles and Circular Sectors
Josephine McCotter@jp.mccotter
Ready to master areas of circles and sectors? This guide breaks down how to calculate these shapes with step-by-step solutions. You'll learn to find areas using formulas, handle different angles, and solve for missing dimensions.
1
of 2
Sign up to see the content. It's free!
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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.
2
of 2Sign up to see the content. It's free!
- Access to all documents
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Area of Circle Sectors
Sectors are like pizza slices cut from a circle. To find their area, you need to know the central angle (θ) and radius . The formula is (θ ÷ 360°) × π × r², which gives you the fraction of the circle's area based on the angle.
When working with sectors, you'll often need to do some angle calculations first. For example, if a circle shows angles of 136° + 136° = 272°, then your sector takes up (272 ÷ 360) × π × 9² ≈ 192.27 square centimeters. For trickier problems, subtract known angles from 360° to find the sector angle.
Some problems may require you to identify the radius correctly. In problem #13, BD is the diameter (18 cm), so the radius is 9 cm. In problem #16, SR represents the diameter (26 m), making the radius 13 m. Always check whether you're given the radius or diameter!
Remember: When calculating sector areas, the angle must be expressed as a fraction of the full circle (360°). So a 90° angle represents 1/4 of the circle's area.
Sometimes you'll need to piece together angles from multiple sections. In problem #14, you need to add angles , then subtract from 360° to get 144° for the desired sector. Using (144 ÷ 360) × π × 5.3² gives approximately 35.30 square kilometers.
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