Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 54
Chapter 11: Perimeter & Area
Lengths and Areas of Rectangles, Triangles and Composite
Shapes


The perimeter of a shape is the total length of its boundary.
You can find the perimeter of a shape by adding the lengths of its sides.
Length l
Width w
w
Perimeter of rectangle = l + l + w + w
= 2(l + w)
l

The area of a shape is a measure of the amount of space it covers.
Typical units of area are square centimetres (cm2), square metres (m2) and square kilometres
(km2).
l
w
Area of rectangle = l  w
You can find the area of a rectangle using the following formula:

Area of rectangle = length  width = l  w
11 Perimeter & Area
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Area of a parallelogram
You can use the rectangle formula to find the area of a parallelogram:
Any side of a parallelogram can be called its base. The perpendicular distance between the base
and its opposite side is called the perpendicular height (or height) of the parallelogram.
5cm
D
C
The
base
of
parallelogram ABCD is
5cm long and the
perpendicular height is
4cm. AE is 2cm.
4cm
A
E
2cm
D
B
3cm
5cm
C
4cm
A
E
4cm
3cm
D
B 2cm
C
4cm
E

5cm
You can cut off the triangle
ADE from one end of the
parallelogram and place it at the
other end. AD is equal and
parallel to BC so they fit
exactly together.
The new shape is the rectangle. The
area of the original parallelogram is
the same as the area of this rectangle,
5  4cm2, which is the base
multiplied by the height.
Area of parallelogram = base  height = b  h
11 Perimeter & Area
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Area of a triangle
There are two ways of finding how to calculate the area of a triangle.
First, if we think of a triangle as half a parallelogram we get
1
 area of parallelogram
2
1
= (base  height)
2
Area of triangle =
Second, if we enclose the triangle in a rectangle we see again that the area of the triangle is half
the area of the rectangle.
1
 area of rectangle
2
1
= (base  height)
2
Area of triangle =
In either case, the equation to find the area of the triangle is the same.

Area of triangle =
11 Perimeter & Area
1
(base  height)
2
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Area of a Trapezium
It is useful to know how to find the area of a trapezium with a simple formula instead of finding
the areas of the two triangles and then add. So, let’s construct an equation to find the area of the
trapezium.
Consider this shape
q
B
C
h
A
p
D
This is a Trapezium. Note that BC is parallel to AD but their lengths are not equal.
BC = q
and
AD = p
We know how to work out the area of triangle ACD and triangle BCD.
Area of triangle ABD =
1
1
(base  height) = p  h
2
2
Area of triangle BCD =
1
1
(base  height) = q  h
2
2
The heights of both triangles are the same, as each is the distance between the parallel sides of
the trapezium.
Therefore
total area of ABCD =
1
1
1
ph  qh  ( p  q)  h
2
2
2
1
the area of a trapezium is equal to (sum of parallel sides)  (distance between them)
2
11 Perimeter & Area
Page 4
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example 1
ABCE is a square of side 8 cm. The total height of the shape is 12 cm. Find the area of ABCDE.
D
E
12 cm
C
8 cm
A
Answer
8 cm
B
In order to find the area of a compound shape, first we have to split it in shapes that we know
how to find the area of. This compound shape can be divided into a square ABCE and a triangle
CDE.
1
So
Area of triangle CDE = (base  height)
2
1
  8  4 2 cm2
2 1
= 16 cm2
Area of Square ABCE = 8  8 cm2
= 64 cm2
So
Total Area
= Area of triangle CDE + Area of Square ABCE
=
16 cm2
+
64 cm2
=
11 Perimeter & Area
80 cm2
Page 5
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Example 2
8cm
2cm
Work out the area of this shape.
7cm
Answer
4cm
First method
Divide the shape into parts whose areas you can find.
This can be done in several ways. One way is:
8cm
2cm
7cm
Area of rectangle A = l  w = 7  4 = 28cm2
1
1
1
Area of trapezium B = a  b h  7  2  4   9  4  18cm 2
2
2
2
B
A
4cm
So the shaded area is 28 + 18 = 46cm2
8cm
Second Method
Add on a small triangle to make a larger rectangle.
2cm
7cm
5cm
Area of large rectangle = l  w = 7  8 = 56cm2
4cm
4cm
1
1
Area of small triangle C =  base  height =  5  4  10cm 2
2
2
So the shaded area is 56 – 10 = 46cm2
Example 3
The area of a triangle is 20 cm2. The height is 8 cm. Find the length of the base.
Answer
Let the base be b cm long.
1
(base  height)
2
1
  b  8 4
2 1
= 4b
=5
8 cm
Area of triangle =
20
20
b
b cm
So, the base is 5 cm long.
11 Perimeter & Area
Page 6
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Exercise 1
1.
Find the area of each of the following trapeziums:
a)
b)
4 cm
8.5 cm
6 cm
3 cm
10 cm
5.5 cm
c)
d)
4 cm
7 cm
9 cm
2.5 cm
18 cm
3 cm
2.
Find the areas of the following triangles. If necessary, turn the page round and look at the
triangle from a different direction.
a)
b)
11 cm
7 cm
14 cm
15 cm
7 cm
6 cm
11 Perimeter & Area
Page 7
Name of Lecturer: Mr. J.Agius
3.
Course: HVAC1
Find the areas of the following parallelograms:
a)
40 cm
b)
20 cm
4.
12 cm
20 cm
9 cm
Find the area of the following figures in square centimetres. The measurements are all in
centimetres.
a)
3
b)
4
12
3
4
4
5
10
12
5.
Find the missing measurements of the following shapes.
a. Triangle
b. Parallelogram
c. Rectangle
Area
Base
24 cm2
36 cm2
1.28 m2
6 cm
720 cm
0.64 m
6.
Find the area of each of the compound shapes.
a)
b)
9 cm
3cm
2 cm
Height
6 cm
4 cm
3 cm
4 cm
11 Perimeter & Area
Page 8
Name of Lecturer: Mr. J.Agius
Course: HVAC1
D
c)
D
d)
A
C
A
C
B
ABCD is a rhombus
AC = 9 cm.
BD = 12 cm.
B
ABCD is a kite
(BD is the axis of symmetry.
The diagonals cut at right angles.)
AC = 10 cm. BD = 12 cm.
7.
For these shapes calculate
(a)
(i) the perimeter
(ii) the area.
(b)
(c)
8.5 cm
6.5 cm
8 cm
6 cm
4 cm
10 cm
4 cm
8.
(a)
6.5 cm
3.5 cm
3 cm
Work out the areas of these shapes correct to 1 d.p.
15.4 m
(b)
4.9 m
5.25 cm
6.15 cm
11 Perimeter & Area
Page 9
Name of Lecturer: Mr. J.Agius
9.
Course: HVAC1
Calculate the area of these shapes correct to 2 d.p.
(a)
(b)
12.4 cm
(c)
7.25 cm
12.7 cm
7.26 cm
6.78 cm
14.2 cm
10.
14.5 cm
The diagram shows the measurements, in inches, of the ‘L’ on an ‘L’ plate. Work out the
area of the ‘L’.
1.5 in
4 in
1.5 in
3.5 in
11.
Work out the area of the shape ABCDEF.
A
30 cm
B
E
F
9.5 cm
7 cm
D
12.
11 cm
C
A landscape gardener designs a layout for a garden with an awkward shape. The diagram
shows his plan. Find the area of the lawn.
2m
5m
3m
Patio 1.6 m
3.4 m
4m
Lawn
Shrubs
3.6 m
11 Perimeter & Area
3m
Flowers
4.6 m
1.6 m
3.6 m
Page 10