The figure is made up of Rectangle ABED and Triangle BCE. AB is 14 centimetres, AD is 9 centimetres and DC is 20 centimetres. Find the area of the figure.
Area of figure = 126 + 27 = 153 cm²
Ans: 153 cm²
Example 1
Rahim has a rectangular card PQRS: PQ is 26 cm and QR is 14 cm. T is a point on PQ with PT = 9 cm. He cuts off Triangle PTS along TS. Find the area of the piece he has left.
Area of the piece left = 364 − 63 = 301 cm²
Ans: 301 cm²
How to solve it
Separate the figure along BE into rectangle ABED and triangle BCE. Both are inside the figure, so their areas are added.
Find the triangle's own base: DE equals AB, 14 centimetres, so EC is 20 minus 14, which is 6 centimetres.
Area of a rectangle is length times breadth: 14 times 9 is 126 square centimetres.
For triangle BCE, EC is the base and BE, 9 centimetres, is the height. Half of 6 times 9 is 27 square centimetres.
Add the two parts: 126 plus 27 is 153 square centimetres.
For a corner cut off a card, subtract: 26 times 14 is 364, half of 9 times 14 is 63, so 301 square centimetres are left.
Add the parts that make a figure. Subtract the part removed from a whole.
For parents
How do you find the area of a composite figure in P5?
This page teaches finding the area of a composite figure made up of rectangles, squares and triangles.
What your child learns here
This page teaches finding the area of a composite figure made up of rectangles, squares and triangles. It is the third outcome of the Primary 5 Area of Triangle chapter and uses both the rectangle and the triangle formula.
Split the figure along a line into shapes whose areas you can find, such as a rectangle and a triangle.
When the shapes together make the figure, add their areas.
When a piece is cut off a whole rectangle, find the whole and subtract the piece.
Each triangle needs its own base and its own perpendicular height; a length on the outside of the figure may not be the triangle's base.
A missing length often comes from opposite sides of a rectangle being equal, as in EC = 20 − 14 = 6 cm.
Does the answer make sense?
A figure made by joining shapes must have more area than any one of its parts, and a piece left after a cut must have less area than the whole card. Areas are in square units: 153 cm² is right, and 153 cm is not an area.
How to practise these questions
Basic questions join a square or rectangle to one or two triangles whose heights are printed, so the areas are added. Intermediate questions either cut a triangle from a rectangular card and ask for the piece left, or give the height of the whole figure so the triangle's height must be worked out. Challenge questions hide a length in the area of a square, a perimeter, a midpoint or equal bands, and some ask for a height when the total area is known. Before calculating, ask your child to say aloud whether each part is added or taken away.
Questions parents ask
What is a composite figure? It is a figure made up of simpler shapes. In Primary 5 these are rectangles, squares and triangles, and its area is found from the areas of those parts.
When should my child add and when subtract? Add when the parts sit side by side to make the figure. Subtract when a part has been cut away from a larger shape.
Why does the lesson split along BE? Splitting there gives a rectangle and a right-angled triangle, and both have lengths that can be read or worked out from the figure.
