Area of Joined Shapes

Not every shape is a rectangle. An L-shaped room is two rectangles joined.

Split it up

Cut the shape into rectangles, find each area, then add them.

Where to split

There is usually more than one place to cut. Any of them gives the same total.

Split an odd shape into rectangles

An L-shape is two rectangles joined. Draw a line to separate them, find each area with multiplication, then add. A shape that looked impossible becomes two easy problems and a sum.

Working out the lengths you were not given

Composite shapes usually withhold some measurements. If the whole top edge is 10 and one part is 6, the other part is 4. Fill in every length on the diagram before calculating any areas — most errors in these problems are missing lengths, not arithmetic.

Sometimes subtracting is easier

An L-shape can also be seen as a big rectangle with a smaller one cut out. Find the big area, find the cut-out area, subtract. For some shapes this is much quicker than splitting. Both approaches are valid — try to see which one the shape suits.