The idea in brief. Cut the figure into rectangles to find its AREA, and slide its sides out to the rectangle that encloses it to find its PERIMETER; the only sides that do not slide are the two edges of a notch, and those are added on. For a stepped figure, the sides shift out to the enclosing rectangle; where a notch is cut in from an edge, the perimeter grows by twice the notch's depth. In the lesson. You know how to find the area of a rectangle: length times breadth. Today, we will find the area of a figure made of two rectangles joined together. Split the figure into rectangles. Find the area of each one, then add them.
Lesson video, with the working
Joined rectangles
4 min 10 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
How do you find the area of L-shaped figures in P3?
This page applies the Primary 3 rule for the area of a rectangle or square to figures made of two or more rectangles joined together, such as L and T shapes.
What your child learns here
This page applies the Primary 3 rule for the area of a rectangle or square to figures made of two or more rectangles joined together, such as L and T shapes. It is a step beyond the syllabus wording, and it builds on the same two outcomes.
A figure made of rectangles can be cut into rectangles that fill it and do not overlap.
The area of each part is length × breadth, and the total area is their sum.
Some side lengths are not labelled and must be found from the sides you can see.
The perimeter of a stepped figure follows the outside edge, not the cuts made inside it.
Does the answer make sense?
When rectangles are joined without overlap, your child's total area must be more than the largest piece on its own. When a corner is cut away, as with an L-shaped card, the area left must be less than the area of the full rectangle it came from.
How to practise these questions
The Basic question practises adding the areas of the pieces that make a figure. The Intermediate questions add figures that must first be split into rectangles, with some lengths found from others. The Challenge questions ask for the perimeter of the joined figure as well, where the shared edges are not part of the boundary. When a joined figure stalls, play its solution film and try it again later from Revision.
Questions parents ask
Are L-shaped figures in the P3 syllabus? The Primary 3 syllabus covers the area of a rectangle or square and the perimeter of rectilinear figures. Figures made up of rectangles and squares are named in the following year's syllabus, so this page applies the P3 rule to them as a first step.
Does it matter where my child cuts the shape? No. Any cut that splits the figure into rectangles with no overlap and no gap gives the same total area. Some cuts make the missing sides easier to find, and the lesson shows one way.
How do I find a side that is not labelled? Look at the side opposite it. In an L shape, the long side at the bottom equals the two shorter sides above it added together, so the missing piece is the long side minus the other one.
