… work out area
Area is the measure of a flat (two-dimensional) surface or a space covered
by an object, such as floorboards or plasterboard. It may be used to work
out, for example:
•
how many floorboards would be needed to cover the floor in a room
•
the number of plasterboard sheets needed for a stud wall partition.
Area is measured in square units, e.g. 5 square metres, or 5 m2. The 2
stands for ‘squared’. An easy way to remember this symbol is to think ‘2’
means length x width (2 dimensions squared).
Finding the area of a rectangle
A rectangle is a shape with four right angles and four sides. The opposite
sides are of equal length.
What’s the area of rectangle measuring 4 metres long and 3 metres wide?
Area of a rectangle =
length x width.
•
Length is 4 m and width is 3m
•
Both measurements are in metres
•
Length x width = 4 x 3 = 12
Make sure that measurements are in the
same units.
•
The area is 12 m2
Multiply the length by the width.
Find out the measurements for length
and width.
Check that the units are correct, e.g. m2
Try these!
Work out the area of these rectangles:
100 mm
40 mm
30 mm
30 mm
Finding the area of an ‘L’ shape
Sometimes, when you measure up for joists, floorboards or plasterboard,
your room or wall will not be a perfect square or rectangle. The instructions
below show how easy it is to calculate the area of odd-shaped surfaces.
Find the floor area of the following room:
4m
8m
3m
6m
Firstly, split the shape into two rectangles:
Make sure that the dimensions are
in the same units.
4m
To work out the area of an Lshape, you split the shape into two
rectangles.
8m
3m
6m
Then work out any unknown lengths:
4m
Work out any unknown lengths by
subtracting known dimensions from
each other. i.e. 6 m – 4 m means the
unknown length must be 2 m.
8m
2m
Work out the area of each rectangle.
3m
6m
Add the areas of the rectangles to
give the total area of the shape.
Area of rectangles = 8 m x 4 m = 32 m2 and 2 m x 3 m = 6 m2
Total area = 32 m2 + 6 m2 = 38 m2
Finding the area of a triangle
You may need to do this when calculating cladding to cover the apex of a
building, or perhaps plasterboarding the end walls of a loft conversion.
Find the area of the following triangle:
5m
4m
Make sure that the dimensions are in
the same units.
The base and height are in centimetres.
Find the area of the rectangle with
the same height and base as the
triangle.
5m
Tip! If it helps, draw in imaginary
lines to so that you can see the full
rectangle and work out the area.
4m
The area of the rectangle is 5 x 4 = 20 m2
The area of the triangle is 20 ÷ 2 = 10 m
Try these!
Work out the area of this triangle:
3m
10m
2
Divide the area of the rectangle by 2.
Finding the area of a circle
You may have to do this when cutting circular shapes for tabletops, or
perhaps working out the quantity of timber decking required for a circular
garden feature.
Find the area of a circle with a radius of 3 m.
The radius of a circle is measured
from the edge of the circle to the
centre of the circle.
3m
Area of a circle =
π (Pi) x radius x radius
Area of a circle =
x radius x radius
Area of the circle = 3.14 x 3 x 3 m2
π is a symbol used in
working with circles.
3.14 x 3 x 3 = 28.26 m2
π = 3.14
Try this!
Pi is always 3.14, no
matter what the object or
radius is.
Work out the area of this circle:
4m