Mathematics 7th grade | UNIT 18: Area‚ perimeter and volume 18.2 Calculating the area and perimeter of rectangles
When you draw a rectangle on a centimetre square grid, you can work out the area of the rectangle by counting squares.
Area = $6c{m^2}$
Instead of counting squares, you can multiply the length of the rectangle by its width to work out the area.
Area = ${\text{3 }} \times {\text{ 2 = 6 c}}{{\text{m}}^2}$
The formula for working out the area of any rectangle is:
area = length $ \times $ width
or $A = l \times w$
The perimeter of a shape is the total distance around the outside of the shape.
You find the perimeter of a shape by adding the lengths of all the sides together.
The perimeter of this rectangle is:
$3 + 2 +3 + 2 = 10cm$
You can see that you are adding two lengths and two widths together.
The formula for working out the perimeter of any rectangle is:
perimeter $ = 2 \times $ length $ + 2 \times $ width
or $P= 2l + 2 w$
Worked example 18.2
Work out the area and the perimeter of this rectangle.
Solution
Area ${\text{ = 6}} \times {\text{4}}$
Use the formula: area = length × width.
${\text{ = 24 c}}{{\text{m}}^2}$
Remember to write the correct units, $c{m^2}$, with your answer.
Perimeter ${\text{ = 2 }} \times {\text{ 6 + 2 }} \times \,\,{\text{4}}$
Use the formula: perimeter $ = 2 \times $ length $ + 2 \times $ width.
$= 12 + 8$
Work out 2 × length and $2 \times $ width first, then add the answers.
$= 20 cm$
Remember to write the correct units, cm, with your final answer.
Exercise 18.2
1) Work out the area and perimeter of each of these rectangles.
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2) A sheet of ${A_5}$ paper is 210 mm long and $148 mm$ wide.
What is the area of a sheet of ${A_5}$ paper?
3) Connor is laying a new patio in his garden.
The diagram shows the dimensions of his patio.
Work out:
a: the area of the patio
b: the perimeter of the patio.
4) A rectangular room has an area of ${\text{12}}{{\text{m}}^2}$'.
The length of the room is $4 m$.
Work out:
a: the width of the room
b: the perimeter of the room.
5) Copy and complete both methods shown to find the area of this rectangle.
Method 1
Width $= 3 mm = 0/3 cm$
Area = ${\text{2 }} \times {\text{ 0}}{\text{.3 = }}.....{\text{c}}{{\text{m}}^2}$
Method 2
Length $= 2 cm = 20 mm$
Area = ${\text{20 }} \times {\text{ 3 = }}......{\text{ m}}{{\text{m}}^2}$
6) The table shows some information about five rectangles A to E.
| Perimeter | Area | Width | Length | Rectangle |
| $6mm$ | $8mm$ | A | ||
| $28c{m^2}$ | $4cm$ | B | ||
| $60{m^2}$ | $12m$ | C | ||
| $22cm$ | $8cm$ | D | ||
| $20mm$ | $1/5mm$ | E |
Copy and complete the table.
7) Keira wants new carpet in her hall.
The hall is a rectangle that measures $4 m$ long by $90 cm$ wide.
Work out the area of carpet that she needs.
8) Oditi and Tanesha are drawing rectangles with whole-number lengths and widths.
Who is correct? Explain your answer.
I can only draw three different rectangles with an area of ${\text{24c}}{{\text{m}}^2}$
There are four different rectangles with an area of ${\text{24c}}{{\text{m}}^2}$