When working with perimeter and area, it is very important not to get confused between the two.
Make sure you understand each one and know the definition of each.
•
This is the total distance right around a shape.
•
Formula for the perimeter of a rectangle: Perimeter = 2(l) + 2(w) (square: 4 x sides)
In this example, we count the total amount of blocks
on the outside edges of the shape.
Perimeter = 5 units + 4 units +
2 units + 2 units + 3 units + 2 units
5+4+2+2+3+2
= 18 units
4
2
5
2
3
2
7cm
3cm
3cm
Perimeter = 2l + 2w
= 2 x (7cm) + 2 x (3cm)
= 14cm + 6cm
= 20cm
7cm
1
Activity 1:
Date: _____________________
1. Look at each shape below.
a) If I walk right around each shape, how far will I travel?
P = 2 x (l +w)
______________________________________
= 2 x (4km +4km)
______________________________________
= 2 x 8km
______________________________________
= 16km
______________________________________
P = 2 x (l +w)
______________________________________
= 2 x (800m + 500m)
______________________________________
= 2 x 1 300m
______________________________________
______________________________________
= 2 600m
P = 12cm + 27cm + 37cm
______________________________________
= 76cm
______________________________________
______________________________________
______________________________________
2
By using my formula / by adding all my sides together / by calculating
b) How did you get your answer? ___________________________________________________
all the sides on the outside together.
____________________________________________________________________________
P = 4 x side / 4 x l / 4 x w
c) Which rule would you use to determine the perimeter of a square? _______________________
____________________________________________________________________________
P = 2 x (l + w)
d) Which rule would you use to determine the perimeter of a rectangle?______________________
_____________________________________________________________________________
Activity 2:
Date: ___________________
Find the missing lengths and calculate the Perimeter:
a)
Perimeter: ___________________________
___________________________
___________________________
___________________________
b)
Perimeter: ___________________________
___________________________
___________________________
___________________________
3
c)
Perimeter: ___________________________
___________________________
___________________________
___________________________
d)
Perimeter: ___________________________
___________________________
___________________________
___________________________
•
This is the size of the floor of a shape.
We calculate the area of a shape by counting the total square units that it
covers (the total blocks in the shape). Firstly, count all the whole squares.
Secondly, count all the half squares together to form whole squares.
In this figure we have 6 whole squares and 8 half squares.
8 half squares = 4 whole squares
6 + 4 = 10 units²
Use the formula to calculate the area of the rectangle.
12 cm
5cm
Area: l x w
= 12cm x 5cm
= 60cm²Type text here
4
Activity 1:
Date: _________________
1. Calculate the area of the following figures:
______________________________
A=lxw
= 6cm x 2cm
______________________________
2
= 12 cm
______________________________
A=lxw
______________________________
______________________________
= 6 cm x 6cm
2
= 36 cm
______________________________
2. Find the missing sides and calculate the Area of each figure.
a)
15cm
A=lxw
A=lxw
3cm ______________________________
= 15cm x 3cm
= 12cm x 10cm
______________________________
2
= 45cm2
= 120cm
______________________________
2
45 + 120 = 165cm
______________________________
______________________________
A=lxw
A=lxw
b)
= 11cm x 2cm
= 7cm x 8cm
______________________________
= 22cm2
= 56cm2
______________________________
2
7cm
22 + 56 = 78cm
______________________________
8cm
5
3. Look at the square below and answer the questions.
5 cm
5 cm
5 cm
5 cm
25 Squares
a) How many squares are inside the square? __________________________________________
2
5 x 5 = 25 cm
b) How can I use the lengths of the sides to arrive at the same answer? _____________________
____________________________________________________________________________
A= l x w
c) Which rule can you use to work out the area of a square? _______________________________
_____________________________________________________________________________
4. Look at the rectangle below and answer the questions that follow:
8m
4m
4m
8m
32 Squares
a) How many squares are inside the rectangle? ________________________________________
2
8 x 4 = 32 m
b) How can I use the lengths of the sides to arrive at the same answer? _____________________
____________________________________________________________________________
A=lxw
c) Which rule can you use to work out the area of a rectangle? ____________________________
____________________________________________________________________________
6
•
Volume can be worked out when an object has three dimensions:
•
Length, width and HEIGHT.
•
Volume is the amount that a container/object holds or can hold.
Volume can be worked out as follows:
Volume = l x w x h
= 5x2x3
= 30cm³
3cm
5cm
2cm
6cm
10cm
Volume = l x w x h
= 10 x 6 x 6
= 360cm³
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Activity 2:
Date: _______________________
1. Look at the rectangular prism and answer the questions below.
10 cm
3 cm
4 cm
a) Use your knowledge of surface area and work out the surface area of the top face of the prism.
A=lxw
___________________________________________________________________________
= 10cm x 3cm
___________________________________________________________________________
2
= 30cm
___________________________________________________________________________
b) Now multiply your answer by the height of the prism to get the volume of the prism.
V = 30cm x 4
___________________________________________________________________________
3
= 120 cm
___________________________________________________________________________
___________________________________________________________________________
2. Work out the volume for each of the following prisms.
a)
20 mm
5 mm
10 mm
V=lxwxh
______________________________
= 20mm x 5mm x 10 mm
______________________________
3
______________________________
= 1 000mm
______________________________
8
5 cm
4 cm
10 cm
10 cm
25 cm
b)
10 cm
V=lxwxh
______________________________
c)
V=lxwxh
_____________________________
= 10cm x 10cm x 10cm
= 5cm x 4 cm x 25 cm
______________________________
_____________________________
3
3
= 1 000cm
______________________________
= 500cm
_____________________________
______________________________
_____________________________
______________________________
_____________________________
d)
300 mm
30 mm
50 mm
V=lxwxh
______________________________
= 300mm x 30mm x 50 mm
______________________________
3
= 450 000mm
______________________________
______________________________
______________________________
9
Activity 1
Date: _________________
Calculate the perimeter and area of the following shapes.
1)
2)
3)
4)
10
5)
6)
7)
P = 10+5+4+2+6+7
= 34cm
A= l x w
= 10x5
= 50cm 2
2
62cm
A=lxw
= 6x2 2
= 12cm
8)
P = 5+5+5+4+8+14+10
= 51m
A= l x w A = l x w A = l x w
= 5x5 2 = 4x4 2
=14 x5
= 25cm = 16cm
= 70cm2
2
111cm2 / 97cm
11
9)
P =13+10+5+10+18+20
=76cm
A= l x w
= 10x13
= 130cm2
A=lxw
= 18x10 2
= 180cm
310cm2
Activity 2
Date______________________
Calculate the perimeter and area by looking at the squares. Each square represents 1cm x 1cm.
1)
P= 2+1+3+2+5+3
= 16cm
2)
P = 3+0.5+3+2+5+3
= 16 1/2 cm
3)
P = 3+0.5+2+6+1.5
=13cm
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