Simple Areas

1
Simple Areas
Definition Area is how much space a shape
takes up
A few types of special Areas
www.mathsrevision.com
Counting Squares
Rectangle
Any Type of Triangle
RAT.
Trapezium
Rhombus and kite
Parallelogram
Composite Area
2
Starter Questions
National 4 EF 1.2b
Q1. Solve the equation below
ao
Q2. Find the missing angles
bo
Q3. Find the average of the numbers below
www.mathsrevision.com
2,5,6,7
Q4. Which is the better deal
or
3
Area Counting Squares
National 4 EF 1.2b
Learning Intention
Success Criteria

1. To understand the term area.

1. To explain area in terms of counting
squares.

1. Find the area by counting squares.

www.mathsrevision.com
4
Area Counting Squares
National 4 EF 1.2b
The area of a shape is simply defined by
the amount of space a shape takes up.
Think of a square measuring 1 cm by 1cm we say it
is
www.mathsrevision.com
1cm2
( 1 square centimetre )
5
Area Counting Squares
National 4 EF 1.2b
Now try Exercise 1 Ch14 (page 163)
www.mathsrevision.com
6
Starter Questions
National 4 EF 1.2b
Q1. What is the time difference 0928 and 1155
Q2.
www.mathsrevision.com
Q3. Convert 23metres to (a) cm (b) mm
Q4. The answer to the question is 180. What is
the question.
7
Area of a Rectangle
National 4 EF 1.2b
Learning Intention
Success Criteria

1. To be able to state area formula for a rectangle.

1. To come up with a formula for the
area of a rectangle.

• Apply formula correctly.
• (showing working)

www.mathsrevision.com

1. Use the formula to solve problems.

• Answer containing
• appropriate units

8
Area of a Rectangle
National 4 EF 1.2b
B
L
B
L
L length
www.mathsrevision.com
L
B
B Breadth
3
1
3
4
3
12
Must learn formula !
3
2
6
9
Area of a Rectangle
National 4 EF 1.2b
Example
Find the area of the rectangle
B 2cm
L 9cm
Area Length x Breadth
A L x B
www.mathsrevision.com
A 9 x 2
A 18 cm2
10
Area of a Rectangle
National 4 EF 1.2b
Example
Find the length B of the rectangle opposite
A 36cm2
B cm
L 12cm
Area Length x Breadth
Balancing Method
A L x B
www.mathsrevision.com
36 12 x B
Remember units
11
Area of a Rectangle
National 4 EF 1.2b
Now try Exercise 2 Ch14 (page 167)
www.mathsrevision.com
12
Starter Questions
National 4 EF 1.2b
Q1. Calculate
110o
Q2. Are the missing angles 70o,40o,40o Explain
www.mathsrevision.com
Q3. Is the HCF of 10 and 36 180 Explain.
Q4. Explain 2 ways of calculating
13
Any Triangle Area
Learning Intention
Success Criteria

1. To know the formula for the area of ANY triangle.

1. To develop a formula for the area of ANY
triangle.
www.mathsrevision.com

• Apply formula correctly.
• (showing working)

1. Use the formula to solve problems.

• Answer containing
• appropriate units

14
Any Triangle Area
Demo
Sometimes called the altitude
h
www.mathsrevision.com
15
Any Triangle Area
Example 1 Find the area of the triangle.
6cm
www.mathsrevision.com
16
Any Triangle Area
National 4 EF 1.2b
Example 2 Find the area of the triangle.
Altitude h outside triangle this time.
10cm
www.mathsrevision.com
17
Area of ANY Triangle
National 4 EF 1.2b
Now try Exercise 4 Ch14 (page 174)
www.mathsrevision.com
18
Starter Questions
National 4 EF 1.2b
Q1. Why is
Q2. What is the time difference 0754 and 1336
Q3.
www.mathsrevision.com
Q4. Convert 45.1 metres to (a) cm (b) mm
Q5. The answer to the question is 90. What is
the question.
19
Area of a Composite
National 4 EF 1.2b
Made up of Simple shapes
Learning Intention
Success Criteria

1. To be able to use knowledge gained so far to find
   the area of more complicated shapes..

1. To use knowledge to find area of more
complicate shapes.
www.mathsrevision.com

1. Show appropriate working.

20
Area of a Composite
National 4 EF 1.2b
Calculate the area of this shape
Total Area
72 30
102cm2
A l x b
A 9 x 8
www.mathsrevision.com
A l x b
A 72cm2
A 6 x 5
A 30cm2
21
Area of a Composite
National 4 EF 1.2b
Calculate the area of this shape
www.mathsrevision.com
22
Area of a Composite
National 4 EF 1.2b
Calculate the area of this shape
Total Area
80 24
104cm2
A l x b
www.mathsrevision.com
A 8 x 10
A l x b
A 80cm2
A 4 x 6
A 24cm2
23
Area of a Composite
National 4 EF 1.2b
Calculate the area of this shape
16cm
Rectangle 1
A l x b
A 16 x 5
5cm
A 80cm2
www.mathsrevision.com
Rectangle 2
A l x b
Total Area
A 6 x 5
80 30 110cm2
A 30cm2
24
Area of a Composite
National 4 EF 1.2b
Now try Exercise 5 Ch14 (page 176)
www.mathsrevision.com
25
Starter Questions
National 4 EF 1.2b
Q1. 40 of 90
Q2. Show that there are 2880 minutes in 2 days
www.mathsrevision.com
Q3. Expand 2( y - 3p) 2y
Q4. Calculate
26
Parallelogram Area
Learning Intention
Success Criteria

1. To know the formula for the area of a
   parallelogram.

1. To develop a formula for the area of a
parallelogram.
www.mathsrevision.com

• Apply formula correctly.
• (showing working)

1. Use the formula to solve problems.

• Answer containing
• appropriate units

27
Parallelogram Area
National 4 EF 1.2b
Important NOTE h vertical height
www.mathsrevision.com
28
Parallelogram Area
National 4 EF 1.2b
Example 1 Find the area of parallelogram.
3cm
www.mathsrevision.com
9cm
29
Area of a Parallelogram
National 4 EF 1.2b
Now try Extension Booklet 2E(a) (page 71)
www.mathsrevision.com
30
Starter Questions
National 4 EF 1.2b
Q1. Find the area of the triangle.
3cm
Q2. Expand out 2w( w - 5) 3w
4cm
www.mathsrevision.com
Q3. Calculate
Q4. Find the LCM of the two numbers 4 and 6
31
Rhombus and Kite Area
Learning Intention
Success Criteria

1. To know the formula for the area of ANY rhombus
   and kite.

1. To develop a single formula for the area of
ANY rhombus and Kite.
www.mathsrevision.com

• Apply formulae correctly.
• (showing working)

1. Use the formula to solve problems.

• Answer containing
• appropriate units

32
Area of a Rhombus
This part of the rhombus is half of the
small rectangle.
National 4 EF 1.2b
www.mathsrevision.com
33
Area of a Kite
Exactly the same process as the rhombus
National 4 EF 1.2b
www.mathsrevision.com
34
Rhombus and Kite Area
National 4 EF 1.2b
Example 1 Find the area of the shapes.
2cm
4cm
5cm
9cm
www.mathsrevision.com
35
Area of a Kite Rhombus
National 4 EF 1.2b
Now try Extension Booklet 2E(b) (page 75)
www.mathsrevision.com
36
Starter Questions
National 4 EF 1.2b
Q1. Find the area of the parallelogram
8
7
Q2. Is the HCF 6 and 24 24 Explain your answer.
www.mathsrevision.com
Q3. Show that 11.5 of 150 is 17.25
Q4. Simplify 3(h -2) h(2 - 4h) -4h2 6h - 6
37
Trapezium Area
Learning Intention
Success Criteria

1. To know the formula for the area of a trapezium.

1. To develop a formula for the area of a
trapezium.
www.mathsrevision.com

• Apply formula correctly.
• (showing working)

1. Use the formula to solve problems.

• Answer containing
• appropriate units

38
Trapezium Area
National 4 EF 1.2b
Two triangles WXY and WYZ
a cm
X
Y
1
h cm
2
www.mathsrevision.com
Z
W
b cm
39
Trapezium Area
National 4 EF 1.2b
Example 1 Find the area of the trapezium.
5cm
4cm
www.mathsrevision.com
6cm
40
Area of a Trapezium
National 4 EF 1.2b
Now try Extension Booklet 6E (page 78)
www.mathsrevision.com