--- title: "Circles: Circumference & Area" description: "Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts" canonical: https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_ source: https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Circles: Circumference & Area Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts Subject: Mathematics · Area: Geometry · Ages 12 to 14 Page: https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_ ## Ready when they can - Calculate the circumference and area of a circle given its radius or diameter - Find the perimeter or area of a composite shape made from rectangles and semicircles - Explain the relationship between π, diameter, and circumference informally ## Lesson: Circles: Circumference and Area You already know the parts of a circle. Now you can use two of them, the radius and the diameter, to measure a circle exactly. The distance around a circle is called its circumference. For any circle, the circumference is always about 3.14 times its diameter. That number is called pi, written as the symbol π. So the formula is C = πd, or if you know the radius instead, C = 2πr, since the diameter is twice the radius. *(drawing: This circle has a diameter of 10 cm. Its circumference is C = π × 10 ≈ 31.4 cm.)* The space inside a circle is its area. The formula is A = πr², so you square the radius first, then multiply by π. Remember: area always uses the radius, never the diameter directly. If you are only given the diameter, halve it first. **Example.** A circular table has a radius of 3 cm. Its area is A = π × 3² = π × 9 ≈ 3.14 × 9 = 28.26 cm². Notice the radius gets squared before you multiply by π. **Tip.** Composite shapes mix straight edges with circular ones. If you see a rectangle with a semicircle stuck on the end, work out the rectangle part and the semicircle part separately, then add them. A semicircle is exactly half of a full circle, so halve the circumference or area formula for that piece. **Recap.** Circumference is π times the diameter (or 2πr), and area is π times the radius squared; break composite shapes into circles, semicircles, and straight parts, then add the pieces. ## Practice 19 questions on this page, each with its working shown. ## Needs first - [Perimeter (age 10+)](https://lightmysky.com/learn/mathematics/perimeter-age-10-mt_MJZA90uc6H) - [Area and volume formulae](https://lightmysky.com/learn/mathematics/area-and-volume-formulae-mt_tAJH5BrpOx) - [Parts of a circle](https://lightmysky.com/learn/mathematics/parts-of-a-circle-mt_xq3YHZ2zeR) ## Opens up - [Volume and Surface Area of Prisms and Cylinders](https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh) - [Arc Length, Sector Area and Segments](https://lightmysky.com/learn/mathematics/arc-length-sector-area-and-segments-mt_z9LIwmfKYJ)