area and perimeter_10_r5
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Starter
• On whiteboards, write down as many units of LENGTH as you can
• Write down as many units for AREA as you can
EXTENSION:What is the perimeter of this rectangle?
Perimeter
Learning Objectives:
Know the key words for perimeter and
the units used
Able to calculate the perimeter of a
rectangle
Able to calculate the perimeter of a
compound shape
09/04/2023
Perimeter
• Perimeter: The distance around the outside of a shape
• To calculate the perimeter, you add together all the sides of a shape
Perimeter
• Example:10cm
3cm
P = 10 + 3 + 10 + 3
P = 26cm
Perimeter
• Calculate the perimeter of the following rectangles:
12cm
4cm
5m
6m
9cm
1cm
5cm
5cm
a)
d)c)
b) EXTENSION:Can you calculate the area of these rectangles?
Perimeter
• Compound shape: a 2D shape made up of many shapes
Perimeter10m
25m
10m
31m
21m
15m
Can I calculate the perimeter of this shape?
I need to find the length of the missing sides first.
Now I can calculate the perimeter by adding up the all the sides.
P = 10 + 15 + 21 + 10 + 31 + 25
P = 112m
Perimeter
• Example:
3cm3cm
9cm 9cm
10cm
5cm
10 – 3 – 3 = 4cm
5cm as it is a rectangle
Perimeter = 5 + 10 + 5 + 3 + 9 + 4 + 9 + 3
Perimeter = 48cm
Starter
• Calculate the perimeter of the following shapes
11cm
5cm
18m
5m
4m
20m
Perimeter
Learning Objectives:
Able to calculate the perimeter of a
rectangle
Able to calculate the perimeter of a
compound shape
Able to calculate the area of a
rectangle
09/04/2023
Your turn…
• Exercise 5A, page 97
Area
• How can I calculate the area of this rectangle?
• Count the squares inside the shape
• Multiply the width by the length
Area of a rectangle
• Area of a rectangle = length x width
4cm
12cm
Area = 4 x 12
Area = 48cm2
Starter
• How many rectangles can you design that have an area of 24cm2?
• Do the sides have to be whole numbers?
Area of Triangles
Learning Objectives:
• Able to calculate the area of a rectangle
• Able to calculate the area of a triangle
• Able to calculate the area of a compound shape
09/04/2023
Area of Triangles
• Area of a triangle = ½ x base x height = ½bh
Base
Height
Area of a Triangle
• Calculate the area of this triangle.
12cm
4cm
Area = ½ x 4 x 12 = 24cm2
Area of Triangles
• Find the area of the shaded triangle BCD.5cm
6cm
4cm
11cm
A
D
CB
Area of ACD = ½ x 9 x 6 = 27cm2
Area of ABD = ½ x 5 x 6 = 15cm2
Area of BCD = 27 – 15 = 12cm2
Your turn…
• Page 104, Exercise 5E, Qs 1 to 4.
Starter
• Complete the worksheet in your workbook– Show all your working out– Remember to use the correct units!
Area of Triangles
Learning Objectives:
• Able to calculate the area of a right angled triangle
• Able to identify the perpendicular height of a triangle
• Able to calculate the area of any triangle
09/04/2023Grade D
Area of Triangles
• Perpendicular – “at right angles to”
Area of Triangles
• Area = base x height2
The perpendicular height
height
base
base
base
heightheight
Area of Triangles
• Find the area of the following triangle.
4cm
10cm
7cm6cm
Area = ½ x 10 x 6 = 30cm2
Area of Triangles
11cm15cm
9cm
12cm
5m
15m
18m8m
Area of Triangles
Learning Objectives:
• Able to calculate the area of a right-angled triangle
• Able to calculate the area of other triangles
• Able to calculate the area of a parallelogram
09/04/2023Grade D
Area of Triangles
17cm12cm
6cm 25m
20m 20m10m
5km
30km
27km
3km
1 2
3
36cm2125m2
45km2
Some work…
• In your workbooks, work through pages 65 and 66.
Home Learning
• Complete the worksheet in your books
• Show all working out
• DUE: Monday 19th September
Starter
• Match the shape to the correct area and perimeter.
• There is one perimeter and one area that don’t have a shape. Draw the shape to match the perimeter and area on the blank card.
Parallelograms and Trapezia
Learning Objectives
• Able to calculate the area of triangles
• Able to calculate the area of parallelograms and trapezia
09/04/2023Grade D
Area of a Parallelogram
12cm
9cm6cm
Area = 6 x 12 = 72cm2
Base
height
Area of Parallelogram = base x perpendicular height
Area of a Trapeziuma
b
h
Area of Trapezium = ½ (a + b) x h
a and b are the parallel sides
Starter
• Calculate the area of these trapezia.15cm
7cm
8cm8cm
14cm
12cm
Area of Compound Shapes
Learning Objectives:
• Able to calculate areas of trapezia
• Able to split up a compound shape
• Able to find the area of a compound shape
09/04/2023Grade D
Compound Shapes
• To find the area of compound shapes, split them up into their composite shapes.
• Find the area of each shape, then add them together
Compound Shapes
5cm
11cm
8cm
2cm
A
B
Area A = 8 x 5 = 40cm2
Area B = 11 x 2 = 22cm2
Total Area = 40 + 22 = 62cm2
Compound Shapes
15cm
7cm1cm
8cm
Your turn…
• Complete the worksheet in your work books.
Starter
• The rectangles below have the same area. Find the value of x.
5cm
8cm
20cm
Circles
Learning Objectives:
• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the
circumference of a circle• Able to calculate the area of a circle
09/04/2023Grade D/C
Circles
• Radius – distance from centre to outside of a circle
• Diameter – distance from one side of the circle to the other, passing through the centre
Circles
6cm 6cm12cm
Diameter = 2 x radius
Radius = diameter ÷ 2
Circles
• Circumference – the distance around the outside of a circle.
• You are going to investigate the relationship between the circumference and the diameter.
Circles
1) Measure the circumference and diameter of the objects and record them in the table.
2) Divide the circumference by the diameter. Write your results in the table
3) Can you spot the common link?
Object Circumference Diameter C ÷ d
Starter
12cm
6cm 7cm
5cm 7cm
11cm
13cm
6cm15cm
18cm
4cm
Calculate the area of each of the following shapes.
Circles
Learning Objectives:
• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the
circumference of a circle• Able to calculate the area of a circle
09/04/2023Grade D/C
Circles
• This relationship between the circumference and diameter is called ‘pi’
• The symbol for pi is ∏
• ∏ = 3.1415926….
• We often use 3.14 as an approximation
• It is found on calculators
Circles
• Circumference = ∏ x diameter
OR
• Circumference = 2 x ∏ x radius
Circles
4cm
Circumference = 2∏r
C = 2 x ∏ x 4
C = 8 x ∏
C = 25.13cm (2dp)
Circles
7cm
Find the circumference of the circle.
C = 2 x ∏ x 7
C = 14 x ∏
C = 43.98cm (2dp)
Starter
• Calculate the area of this trapezium
• Calculate the circumference of this circle4cm
8cm11cm
10cm
6cm
9cm
Circumference
Learning Objectives:
• Able to calculate the radius and diameter of a circle• Able to use a calculator to find the
circumference of a circle• Able to calculate the area of a circle
09/04/2023Grade D/C
CirclesIf I want to find the circumference of these circles, which formula should I use?
6cm
14cm
C = 2 x ∏ x rC = 2 x ∏ x 6C = 12 x ∏
C = 37.7cm (1dp)
C = ∏ x dC = ∏ x 14
C = 43.98 (2dp)
Circles
• Page– Exercise– Questions
Starter
• On your whiteboard, calculate the circumference of the following shapes.
9cm
6cm
10cm
Area of Circles
Learning Objectives:
• Able to calculate the circumference of a circle
• Able to calculate the area of a circle given the radius
• Able to calculate the area of a circle given the diameter
09/04/2023Grade C
Area of Circles
• Area = ∏ x radius2
• Area = ∏r2
radius
Area of Circles
• Area = ∏r2
• Area = ∏ x 42
• Area = ∏ x 4 x 4
• Area = 16 x ∏
• Area = 50.27cm2
4cm
Areas of Circles
7cm
Area of Circles
• Radius = 18 ÷ 2 = 9cm
• Area = ∏ x 92
• Area = 81 x ∏
• Area = 254.47cm2
18cm
Area of Circles
12cm
Your turn…
• Page 364 – 366– Exercise 16C– Questions 1, 3, 5, 6, 7*, 9*
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