1. Shape and Space Rectangles The aim of this unit is to teach pupils to:
Identify and use the geometric properties of triangles, quadrilaterals and other polygons to solve problems; explain and justify inferences and deductions using mathematical reasoning
Understand congruence and similarity
Identify and use the properties of circles
Material in this unit is linked to the Key Stage 3 Framework supplement of examples pp
Rectangles

2. Area
The area of a shape is a measure of how much surface the shape takes up.
For example, which of these rugs covers a larger surface?
Rug B
Rug A
Rug C
Discuss how we can compare the area of the rugs by counting the squares that make up each pattern.
Conclude that Rug B covers the largest surface.

3. Rectangles
The perimeter of a rectangle with length l and width w can be written as: l w
Perimeter = 2l + 2w or
Perimeter = 2(l + w)
The area of a rectangle is given as:
Area = lw

4. Area of a rectangle Area is measured in square units.
For example, we can use mm2, cm2, m2 or km2.
The 2 tells us that there are two dimensions, length and width.
We can find the area of a rectangle by multiplying the length and the width of the rectangle together.
length, l
width, w
Area of a rectangle
= length × width
= lw
This formula should be revision from key stage 2 work.

5. Area of a rectangle What is the area of this rectangle? 4 cm 8 cm
Area of a rectangle = lw
The length and the width of the rectangle can be modified to make the arithmetic more challenging.
Different units could also be used to stress that units must be the same before they are substituted into a formula.
= 8 cm × 4 cm
= 32 cm2

6. Squares
When the length and the width of a rectangle are equal we call it a square. A square is just a special type of rectangle.
The perimeter of a square with length l is given as: l
Perimeter = 4l
The area of a square is given as:
Area = l2

7. Area of shapes made from rectangles
How can we find the area of this shape?
We can think of this shape as being made up of two rectangles.
7 m
Either like this … A
10 m
15 m
… or like this.
8 m
Label the rectangles A and B. B
5 m
Area A = 10 × 7 = 70 m2
Discuss ways to divide this composite shape into rectangles.
A third possibility not shown on this slide would be to take the square of area 15 m × 15 m and to subtract the area of the rectangle 10 m × 8 m.
This gives us 225 m2 – 80 m2 = 145 m2.
15 m
Area B = 5 × 15 = 75 m2
Total area = = 145 m2

8. Area of shapes made from rectangles
How can we find the area of the shaded shape?
We can think of this shape as being made up of one rectangle cut out of another rectangle.
7 cm A
3 cm
Label the rectangles A and B.
8 cm
4 cm B
Area A = 7 × 8 = 56 cm2
Discuss ways to find the shaded area before revealing the solution.
Area B = 3 × 4 = 12 cm2
Total area = 56 – 12 = 44 cm2

9. Shapes made from rectangles
Modify the compound shape on the board and discuss the various ways to find its area by splitting it into two rectangles or by subtracting a rectangle.
Turn off the square grid and hide the lengths of some of the sides by clicking on them. Discuss how the lengths of these missing sides can be found and use these lengths to find the perimeter and the area.