CALCULATING PERIMETER
WHAT IS PERIMETER?
Perimeter is the total length or distance around a figure.
HOW DO WE CALCULATE PERIMETER?
The formula one can use to calculate perimeter depends on the type of shape it is.
1. Square
All 4 sides are equal. Hence, the formula is 4 x 𝑙𝑙
P
2cm
= 4 x 𝑙𝑙
= 4 x 2cm
= 8cm
2cm
2. Rectangle
2 pairs of opposite sides are equal
Hence, the formula is 2 x (𝑙𝑙 + b)
P
4cm
= 2 x (𝑙𝑙 + b)
= 2 x (4cm + 1cm)
1cm
= 2 x 5cm
= 10cm
3. Irregular Shape
As the sides may be different, the formula is simply to add the sides together.
2,5cm
P= sum of sides
2,5cm
= 2,5cm + 2,5cm + 3,5cm + 2,5cm + 6cm + 5cm
= 22cm
3.5cm
5cm
2,5cm
1
6cm
Exercise 1
1. Calculate the perimeter of each of the shapes below:
1.1
1.2
1.3
3,5m
4m
6m
1,5m
8m
1.4
7m
1.5
1.6
25m
4,87cm
60m
3,4cm
20mm
80m
100m
2,65cm
2. The perimeter of a square is 169cm. What is the length?
3. The perimeter of a rectangle is 55cm. If the length is 15cm, what is the breadth?
4. A swimming pool is 6,5m long and 3,5m wide. The paving around the pool is 1,5m
wide. If this entire area is to be fenced off, how much fencing is required?
5. Study the diagram of a piece of farming land below:
24km
29km
6km
23km
34km
a. What is the perimeter of the land?
b. How long will it take the farmer to drive around the boundary of the land if he
travels at an average speed of 40 km/h?
c. If the farmer leaves at 09h30, at what time will he complete his drive?
6. A sports field is 200m long and 138m wide. How many times must you jog around the
field if you want to jog at least 10km?
2
CONCEPT : CALCULATING AREA
WHAT IS AREA?
Area is the size of a surface that is enclosed by a perimeter or boundary.
HOW DO WE CALCULATE AREA OF SQUARES AND RECTANGLES?
•
A 2D shape has 2 dimensions: length and breadth. To determine what the area
is, we use the formula: AREA = Length x Breadth
•
The answer will always be a square measurement (e.g. mm2, cm2, m2, km2)
Example:
= 𝑙𝑙 x b
= 6,5m x 2m
= 13m2
A. HOW DO WE CACULATE THE AREA OF IRREGULAR SHAPES?
20
•
In the irregular shape, one cannot simply
apply the formula A = 𝑙𝑙 x b as there is more
than 1 given length or breadth.
25
•
30
Sub-divide the shape into squares or
rectangles, and then apply the formula to
50
each sub-divided shape. Now add the
25
50
answers together.
Area of A = 𝑙𝑙 x b
= 50m x 20m
= 1 000m2
3
20
50
A
30
B
25
Area of B = 𝑙𝑙 x b
= 50m x 30m
= 1500m2
Total area: 1 000m2+ 1 500m2 = 2 500m2
EXERCISE 2
1. Calculate the area of each of the shapes below: All measurements in m.
5,5
8
1.1
1.2
12,3
30
1.3
1.4
80
20
20
40
100
60
1.5
19
6
20
5
4
2. A home owner wants to carpet her lounge, which is 6,5m long and 4,25m wide. If
the carpet company charges R89 per square meter of carpet, how much will she
have to pay?
3. Your school needs to acquire new soccer fields. A soccer field is 100m by 50m. If it
purchases a square piece of land that has a length of 250m, how many soccer
fields can it fit on the land?
4. Study the diagram below:
7m
4m
Roses
3m
5m
A gardener wants to pave the border around his rose garden.
a. How much soil does he need for the rose garden?
b. How much paving will he need?
5. Terrence decides to tile his kitchen floor. The floor is 3m long and 2,8m wide.
a. How many tiles will he need if each tile measures 20cm x 20cm.
b. How much does he have to pay if the tiles cost R491,75 /m2?
6. If the area of a rectangle is 42cm2 and its length is 60mm, what is its breadth?
7. I want to purchase a rectangular mirror which is 6m long and 4m wide. The frame
around the mirror will extend 1,5m on each side. What is the total area of the
frame?
8. The area of a room is 20,65m2. What is the length of the room if the breadth is
2,4m?
5
CONCEPT :AREA OF TRIANGLES
•
•
Previously, you saw that the formula for the area of a square or rectangle is A = 𝑙𝑙 x b
•
Can you see that the rectangle can be divided so that 2 identical triangles are formed?
•
What does this tell you about the relationship between the triangles and the rectangle?
•
Do you agree that the rectangle is twice the size of the triangle, or that one triangle is
Now study the diagram below:
half the size of the rectangle?
•
This means that the area of the triangle is half the area of the rectangle.
•
Hence, to work out the area of triangle, the formula used is ½ x (b x h).
Example:
A
B
Area of ACD = ½ x (b x h)
3m
= ½ x (6cm x 3cm)
= ½ x 18cm
= 9cm
C
D
6m
EXERCISE 3
1. Calculate the area of each of the following triangles:
12cm
1.1
1.2
3cm
5cm
3cm
6
1.3
1.4
7m
20mm
27m
75mm
2.
Base
Height
A
30cm
45cm
B
16cm
C
3,1cm
D
Area
80cm2
9,4cm
12cm
186cm2
7
CONCEPT : CALCULATING VOLUME
DEFINITION OF VOLUME
•
Volume is the amount of space taken up by a 3D object
•
The units of measurement used to calculate volume are m𝑙𝑙, 𝑙𝑙 and cubic
measurements (e.g. m3)
FORMULA FOR VOLUME
1. A cube or rectangular prism
The formula for volume is: V = 𝑙𝑙 x b x h
Example:
V = 𝑙𝑙 x b x h
= 18m x 4m x 6m
6
= 192m3
4
18
2. A right-angled triangular prism
Step 1: Determine the area of the bottom face of the prism
Step 2: Multiply your answer by the height of the prism
i.e.
V = area x height
Area of the triangle
= ½ (b x h)
= ½ (3cm x 2cm)
= ½ of 6cm
= 3cm2
3
3,5
Volume = 3 x 3,5cm3
= 10,5cm3
2
8
EXERCISE 4
Calculate the volume of each prism below:
1)
2)
6cm
4cm
6cm
6cm
6cm
12cm
3)
4)
3,4m
65mm
4,1m
5mm
7,3m
15mm
5)
6)
32m
2,1km
5km
75m
0,8km
8m
9