Area of composite shapes

Split, find, add

A composite shape is made by joining two or more simple shapes, most often rectangles. The L-shaped floor below is really two rectangles sitting together. You cannot measure its area in one multiplication, but you can measure each rectangle and add the results.

The method has three steps. First split the shape into rectangles. Then find the area of each rectangle with length × width. Finally add the areas together. The total is the area of the whole shape.

Choose a helpful split

Most composite shapes can be split in more than one way. For an L-shape, you can cut it into a tall rectangle and a short rectangle, or into a wide rectangle and a small one. Both ways give the same total area, so choose the split that makes the numbers easiest to work with.

The parts must not overlap, and together they must cover the whole shape. If two rectangles share a strip, that strip is counted twice and the answer is too big. Sketch the split before you start so you can see where the parts meet.

Removing a piece

Sometimes subtraction is quicker than addition. If a small shape has been cut out of a larger rectangle, find the area of the whole rectangle, find the area of the missing piece, then subtract. A 10 m by 8 m wall with a 3 m by 2 m window has an area of 80 - 6 = 74 m² of paint work.

Addition and subtraction are two views of the same idea. Adding the parts builds the shape up; subtracting the hole cuts it down. Use whichever matches the drawing in front of you, and always check that the parts together account for every square in the shape.

Composite shapes in real life

Real rooms are rarely plain rectangles. Kitchen floors, garden beds and swimming pool decks often have an L, a T or a step in them. Splitting the shape at the step turns a hard problem into two easy multiplications, and each part keeps its own unit: square metres for a floor, square centimetres for a tile.