Mathematics
Advanced
50 mins
Teacher/Student led
+85 XP
What you need:
IWB/Projector/Large Screen
Scissors

Composite Shapes: Break It Into Rectangles and Triangles

Learn to find the area of composite shapes by breaking them into rectangles and triangles, working out each piece's area, and adding them together to find the whole.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is an L-shaped patio. It is not a rectangle, and it is not a triangle, so our area rules don't fit it straight away.

    Have a look: how could you break this shape into pieces you already know how to measure?

    2 - Watch and Notice ~9 mins

    Composite shapes are not single rectangles or triangles, so one area rule will not fit the whole shape. We draw a straight split line to break the shape into pieces we already know, work out each sub-area, then add those sub-areas for the total.

    Worked example: an L-shape

    Here is an L-shaped patio. One straight split line turns it into two rectangles:

    • Rectangle A is 6 cm by 4 cm. Area = 6 × 4 = 24 cm².
    • Rectangle B is 3 cm by 2 cm. Area = 3 × 2 = 6 cm².

    Add the sub-areas: 24 + 6 = 30 cm². That is the area of the whole L-shape.

    The same method works when a piece is a triangle. A triangle fills exactly half of the rectangle that encloses it on the same base and height, so a triangle's area is base × height ÷ 2. That half can be a decimal, and that is fine.

    On the interactive, build a rectangle or a triangle on the grid and read its area. Notice how two sub-areas add to make the whole composite total.

    3 - Try It Together ~11 mins

    Key point

    We work through these composite shapes together on the board. One pupil comes up and works the shape; everyone else watches and agrees or corrects out loud.

    • L-shape
    • T-shape
    • House-shape

    Each time, we draw the split line, name the two pieces, and add the sub-areas.

    4 - Sketch the Split in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, sketch each composite shape and draw the split-line that breaks it into its known parts. Label each sub-area with its dimensions, then total at the bottom.

    5 - Cut and Total a Paper L-shape ~10 mins

    Key point

    Take your paper L-shape. Draw one straight split line so you have two rectangles you can cut apart.

    Cut along the line, measure the sides of each rectangle in centimetres, work out the two areas, then add them for the whole L-shape.

    Hands-on Task

    Pupil practice
    Module 4 · Measures: Length, Mass, Capacity, Area, Volume Measures
    Lesson 50 · Composite Shapes: Break It Into Rectangles and Triangles
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