Area & perimeter of composite figures - Ganily

A composite figure is just simple shapes joined together, so there is never a new formula to learn — only a decision to make. You can SPLIT the figure into rectangles and add their areas, or take the whole rectangle that boxes it in and SUBTRACT the piece that is missing. Both always work; pick whichever the given lengths suit. The real work in a PSLE composite question is the lengths that are not written on the figure: opposite sides of the bounding rectangle must add up to the same total, so a missing edge is always a subtraction away. And one result surprises everybody — cutting a corner out of a rectangle changes its area but not its perimeter.

Worked example

Problem The figure is a rectangle 16 cm by 10 cm with a 4 cm by 3 cm corner cut out. Find (a) its area and (b) its perimeter.

Start with the whole rectangle: 16 × 10 = 160 cm².

The corner that was removed is 4 × 3 = 12 cm².

(a) Subtract it: 160 − 12 = 148, so the area is 148 cm².

(b) For the perimeter, walk round the edge. The two cut edges, 4 cm and 3 cm, replace exactly the 4 cm and 3 cm they removed — so the distance round is still 2 × (16 + 10) = 52, that is 52 cm.

Watch out Cutting a corner out of a rectangle does NOT shrink its perimeter. Almost everyone subtracts from the perimeter too, and loses the mark.

Practise this skill →