--- title: "Perimeter (age 10+)" description: "Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically" canonical: https://lightmysky.com/learn/mathematics/perimeter-age-10-mt_MJZA90uc6H source: https://lightmysky.com/learn/mathematics/perimeter-age-10-mt_MJZA90uc6H.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`. # Perimeter (age 10+) Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically Subject: Mathematics · Area: Measurement · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/perimeter-age-10-mt_MJZA90uc6H ## Ready when they can - Draw two rectangles with area 24 cm² but different perimeters - Find two shapes with perimeter 20 cm but different areas - Explain why a long thin rectangle and a square can have the same area but different perimeters ## Lesson: Same area, different perimeter You already know how to find a perimeter by adding every outside edge. Area tells you how much space is inside a shape. That helps when two rugs cover the same floor but need different lengths of edge trim. Two shapes can share the same area and still have different perimeters. In a rectangle, a length plus a width equals half the perimeter. *(drawing: This rectangle is 4 cm by 9 cm. Add its four sides for the perimeter: 4 + 9 + 4 + 9 = 26 cm. Its area is 4 x 9 = 36 square cm.)* **Example.** Now look at a rectangle that is 3 cm by 12 cm. Its area is 3 x 12 = 36 square cm, the same as before, but its perimeter is 30 cm, four more. For two rectangles with the same area, the one closer to a square always has the smaller perimeter. The same perimeter can hide different areas: a 4 by 9 and a 6 by 7 rectangle both go around 26 cm, but their areas are 36 and 42 square cm. **Tip.** For the same area, a rectangle shaped more like a square always has a smaller perimeter than a long, thin one. When you compare two shapes, check area and perimeter separately. Matching one does not mean the other matches too. **Recap.** Same area does not mean same perimeter, and same perimeter does not mean same area, so check each one on its own. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Area and perimeter of rectangles](https://lightmysky.com/learn/mathematics/area-and-perimeter-of-rectangles-mt_eiB3-6pu6a) - [Perimeter of Compound Shapes](https://lightmysky.com/learn/mathematics/perimeter-of-compound-shapes-mt_n0AlyLQwC9) ## Opens up - [Circles: Circumference & Area](https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_)