Area of compound shapes
Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas
What a learner can do afterwards
- 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?
The lesson
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.
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.
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.
Split a compound shape into rectangles, find each rectangle's area, then add them together for the total.
Watch it
Where it sits
Learn first
This opens up
Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.