--- title: "Area of compound shapes" description: "Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas" canonical: https://lightmysky.com/learn/mathematics/area-of-compound-shapes-mt_eMtV6tBSJm source: https://lightmysky.com/learn/mathematics/area-of-compound-shapes-mt_eMtV6tBSJm.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`. # Area of compound shapes Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas Subject: Mathematics · Area: Measurement · Ages 8 to 9 Page: https://lightmysky.com/learn/mathematics/area-of-compound-shapes-mt_eMtV6tBSJm ## Ready when they can - Decompose an L-shape into two rectangles, find each area, and add them - Find the area of a floor plan shaped like a T by splitting into rectangles - Solve: A room is L-shaped (3m×5m plus 2m×4m) — what is the total area? ## Lesson: Finding the area of compound shapes A compound shape is made of two or more rectangles joined together, like an L-shape or a T-shape. You already know that area is the amount of space inside a shape, and area is additive: you can split a shape into parts and add up their areas to get the whole. *(drawing: This rectangle has 3 rows of 4 squares. Area = 3 x 4 = 12 square units. That is the building block for compound shapes.)* **Example.** A room is L-shaped. Draw one straight line to split it into two rectangles: one is 3m by 5m, the other is 2m by 4m. First rectangle: 3 x 5 = 15 square meters. Second rectangle: 2 x 4 = 8 square meters. Total area: 15 + 8 = 23 square meters. **Tip.** Draw your split line first, then label the sides of each rectangle before you multiply. Check that your rectangles do not overlap and together cover the whole shape, or your total will be wrong. **Recap.** Split a compound shape into rectangles, find each rectangle's area, then add them together for the total. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Rectangle area by multiplying](https://lightmysky.com/learn/mathematics/rectangle-area-by-multiplying-mt_GzcJEVkNRn) ## Opens up - [Perimeter of Compound Shapes](https://lightmysky.com/learn/mathematics/perimeter-of-compound-shapes-mt_n0AlyLQwC9)