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Worksheet 69: Area of composite shapes
Worksheet 69
Learning Number Level 2
Area of composite shapes
To find areas of composite shapes with straight edges:
Example 1
●
split the shape into rectangles and triangles;
●
find the areas of the individual bits;
●
add or deduct the areas to get the total area.
We use formulae to calculate area.
breadth
RECTANGLE
Area = length × breadth
length
length
SQUARE
Area = length × length
Note
length and breadth
in same units
length
Keep the units the
same.
1
If a rectangle measures 5m by 3m, its area is 5 x 3 = 15 m2 (square
metres).
●
If a square is 12 mm along each side, its area is 12 x 12 = 144 mm2
(square millimetres).
See how all the measurements are in the same ‘family’ –
nt
Hi
●
lengths in metres (m) give area in square metres (m2)
lengths in millimetres (mm) give area in square millimetres (mm2).
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Learning Number Level 2
Worksheet 69: Area of composite shapes
More complicated shapes can often be split into rectangles, like this:
10.5 m
C
Setting out is
3.5 m
it easier to total your
6m
important as it makes
A
2m
nt
Hi
3.8 m
B
individual areas and
find any mistakes.
3m
4m
Area A = 6 × 4 = 24 m2
Area B = 3.5 × 1.8 = 6.3 m2
Area C = 3 × 3.8 = 11.4 m2
Total area = A + B + C = 41.7 m2
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Worksheet 69: Area of composite shapes
Learning Number Level 2
Or we can treat them as larger rectangles with smaller rectangles or
squares removed, as below.
13 m
8.5 m
C
A
B
3m
3m
3.5 m
3.5 m
8.5 m
3m
3m
Shaded area = area of large rectangle – (total area of A + B + C)
Area of large rectangle = 13 × 12 = 156 m2
Area A = 3 × 3.5 = 10.5 m2
Area B = 3 × 3.5 = 10.5 m2
Area C = 3 × 3 = 9 m2
Total area of A + B + C = 30 m2
Area of shaded area = 156 m2 – 30 m2 = 126 m2
3
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Learning Number Level 2
Worksheet 69: Area of composite shapes
Make sketches of these diagrams and calculate the shaded areas.
Exercise 1
Where there are decimals in an answer, round the final answer to two
decimal places. In some cases, you may have to work out missing
measurements before you start.
3.10 m
1.82 m
0.71 m
4.00 m
1.94 m
2.41 m
3.62 m
2.91 m
3.10 m
1.68 m
2
4.71 m
1.21 m
1
4.00 m
2.89 m
3
4
12.2 m
7.3 m
4.6 m
3.4 m
5.8 m
2.3 m
3.1 m
11.8 m
3m
1m
5
6
11.5 m
6.5 m
5m
8m
12 m
8m
6m
2.4 m
5m
2.3 m
1m
3.1 m
1.8 m
2.8 m
3.2 m
3.1 m
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Worksheet 69: Area of composite shapes
Learning Number Level 2
Area of a triangle
Sometimes, the shapes might be triangular.
Example 2
It is quicker to work out the area of a triangle by this rule:
Area of triangle =
1
2
× base × height
The base can be any side.
The height is the line from the base to the opposite corner.
Example:
Area of triangle
=
1
2
× 10 × 3
=
1
2
× 30
= 15 cm2
height
3 cm
base
10 cm
Exercise 2
1
Find the areas of these triangles.
(a)
(b)
12
2 cm
8 cm
5
cm
25
cm
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Learning Number Level 2
Worksheet 69: Area of composite shapes
2
Find the total areas of these shapes.
1m
(a)
(b)
4m
3.5 m
8m
5m
(c)
3m
2m
4m
Exercise 3
Find the area of the gable end of this building.
5m
3.5 m
6m
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Worksheet 69: Area of composite shapes
Learning Number Level 2
Area of a circle
nt
Hi
π (pronounced pie)
Use the formula: π × radius × radius
is usually rounded to
3.14, or 3.142.
2.5 m
table
The radius is 2.5 ÷ 2 = 1.25 m.
nt
Hi
radius
The radius is half the diameter.
The surface area of the table is:
π × radius × radius
3.14 × 1.25 × 1.25
= 4.90625 m2.
Exercise 4
7
Calculate the surface area of the table above using π = 3.142
(to 3 decimal places).
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Learning Number Level 2
Worksheet 69: Area of composite shapes
Sometimes you have composite shapes that consist of, say, rectangles
and circles (or semi-circles). For example, an ironing board:
Example 3
Find the surface area of the shape below, using π = 3.142.
90 cm
1.6 m
The two ends are semi-circular, with diameter 90 cm = 0.9 m.
nt
Hi
Note the change to
common units of
1
Area of rectangle = 1.6 × 0.9 = 1.44 m2
2
Area of semi-circles = area of a full circle with radius 0.9 ÷ 2
= 0.45 m.
measurement.
A = π r2 = 3.142 × 0.45 × 0.45 = 0.64 m2 (2 decimal places)
Total area = 1.44 + 0.64 = 2.08 m2
Exercise 5
Find the surface of the ironing board shown below. (Use π = 3.142.)
95 cm
1.2 m
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