WJEC MATHEMATICS
INTERMEDIATE
SHAPE AND AREA
AREA, SURFACE AREA, AND
NETS
1
Contents
Area from Squares
Basic Area of 2D Shapes
Compound Area
Nets
Surface Area
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
2
Area from Squares
When given a shape over squared paper you find the area by
counting the squares that the shape covers.
Only count squares that are roughly half a square or larger
Example
Find the area of the following shape is each square is 2mm by 2mm
So in this example, the square covers 17 squares. The area of each
square is 4mm2 so the area of this shape is 17 x 4 = 68mm2
Remember:
The units of area will always be 'squared'. e.g. mm2, cm2,
m2, km2
3
Exam Question G21
1.
2.
4
3.
4.
5
Basic area of 2D Shapes
Squares and Rectangles
To calculate the area of a square or rectangle use the formula;
Example
Parallelograms and Rhombus
The area of a parallelogram and rhombus is calculated using the
formula
Example
Trapezium
To calculate the area of a trapezium, use the formula;
and
are
ALWAYS the
parallel sides
(Remember,
parallel lines
where
are like train
tracks)
6
Example
Note: A trapezium can look different from the one above. The
following are all different forms of a trapezium
Triangles
To calculate the area of a triangle, use the formula;
Careful
Make sure you use the perpendicular height and not a 'sloped' side
7
Exercise G11
Find the area of the following shapes
2.
1.
3.
4.
5.
7.
6.
5.
10.
8.
9.
13.
11.
12.
14.
16.
15.
17.
8
Exam Questions G22
1.
2.
3.
9
Compound Shapes
Compound shapes are shapes made from multiple simple shapes.
To find the area of compound shapes you will need to find the basic
shapes you can use .
Example 1
Consider the following shape.
This shape could have been
made from a large square
with a triangular piece cut
from the corner.
This means we can calculate the area:
6cm
3cm
2cm
6cm
Total Area;
10
Example 2
Consider the following shape
This shape can be split into
two rectangles, then we can
calculate the area of the two
sections separately, adding
them together.
Splitting them into two sections (Label one of them X and another Y)
5m
7m
Before finding the areas of
these shapes we will need to
fill in the lengths of missing
sides
Total Area;
11
Exercise G12
1.
2.
3.
12
4.
5.
6.
13
Exam Questions G23
1.
2.
14
Nets
A net of a 3D shapes is what that shape would look like if it were
'unfolded'.
Examples
15
Exercise G13
Match the shape to correct net
Cone
Cylinder
Tetrahedron
Cube
Square based
pyramid
Triangular Prism
Cuboid
16
Exam Questions G24
1.
2.
3.
17
Surface Area
Nets are useful when calculating surface area. The surface area of a
shape is the total area (sum) of all the faces of the shapes.
Example 1
Area of the top/bottom
Area of the front/back
Area of the sides
The net of this shape consists of 6 sides
So, the total surface area
Example 2
You may be asked to
calculate this side first.
See the booklet
'Pythagoras'
Careful!
1m = 100cm
The net of this shape consists of 5 sides
So, the total surface area
18
Example 3
When this side is
'unwrapped' it forms a
rectangle.
One side length of this
rectangle will be 10cm and
the other will be the
circumference of the circle
See the booklet on
'Circles' for help with
area and circumference
of circles
The net of this shape consists of 3 sides
Exercise G14
1.
19
2.
3.
20
4.
21