Area-of-a-parrallelogram-and-a-trapezium

1. 15.2 The area of a parallelogram and a trapezium
LO:
What I should learn:
Is the answer to:
Work out the area of
this shape.
Area Base Perpendicular Parallelogram Trapezium Trapezia
Calculate the area of a parallelogram and trapezium.
Keywords
Is the answer to:
Find the parallelogram.
Is the answer to:
Work out the area of the
shaded trapezium.

2. Area of a Parallelogram and Trapezium
Starter:
Find the area of these triangles
4cm
6cm 5cm
8cm
1cm
7cm
12cm2
20cm2
3.5cm2

3. Area of a Parallelogram and Trapezium
Recall:
What is the area of this rectangle?
4cm
6cm

4. Area of a Parallelogram and Trapezium
Investigation:
Cut the shape like this
4cm
6cm

5. Area of a Parallelogram and Trapezium
Investigation:
What is the area of this rectangle?

6. Area of a Parallelogram and Trapezium
Investigation:
Cut the shape like this

7. Area of a Parallelogram and Trapezium
Investigation:
What is the area of this parallelogram
4cm
6cm

8. Area of a Parallelogram and Trapezium
Formula:
The formula for the area of a parallelogram is:
Height (h)
Base (b)
h
b
Area 


9. Area of a Parallelogram and Trapezium
Example:
Find the area of this parallelogram
5cm
4cm
h
b
Area 

4
5

Area
2
20cm
Area 

10. Area of a Parallelogram and Trapezium
Example:

11. Activity 1:
Find the area of the following parallelograms
1
Find the missing lengths of these parallelograms when given the area
2
Find the area of this shape
3
a b c d
a b c d
5cm
3cm
7mm
7mm 8m
5m
4.5cm
3cm
6cm
a 24cm2
b
5cm 35cm2
c
10cm
46cm2 d
4.5mm
18mm2
10cm
8cm
5cm
6cm
4cm
Problem
Solving
Below illustrates a garden which needs to be
seeded with grass. The grass seeds costs
£8.50 per packet and covers 15m2.
Work out the cost to cover the garden with
grass seeds.
8m
5m
15cm2
49mm2
40m2
13.5cm2
4cm 7cm
4.6cm 4mm
41cm2
40m2
3 packs
£25.50

12. Area of a Parallelogram and Trapezium
Investigation:
Here are two trapeziums that are the same
B
A
B
A
A
B
h

13. Area of a Parallelogram and Trapezium
Investigation:
Here are two trapeziums that are the same
B
A
h
A
B

14. Area of a Parallelogram and Trapezium
Investigation:
Creates a Parallelogram
B
A
h
A
B
h
b
a
Area 

 )
(

15. Area of a Parallelogram and Trapezium
Investigation:
Creates a Parallelogram
B
A
h
A
B
h
b
a
Area 

 )
(
However area of the trapezium is
half the size:
h
b
a
Area 


 )
(
2
1

16. Area of a Parallelogram and Trapezium
Formula:
The formula for the area of a trapezium is:
Height (h)
b
h
b
a
Area 


 )
(
2
1
a
Area = ½ the parallel sides times by
the distance between the two sides

17. Area of a Parallelogram and Trapezium
Example:
Find the area of this trapezium.
5cm
4cm
h
b
a
Area 

 )
(
2
1
4
)
5
3
(
2
1




Area
2
16cm
Area 
3cm

18. Area of a Parallelogram and Trapezium
Exercise:

19. Let’s play ?
• https://www.transum.org/Maths/Exerci
se/Trapezium/

20. Activity 2:
Find the area of the following trapeziums
1
Find the missing lengths of these trapeziums when given the area
2
Find the area of this shape
3
a b c
a b c
8cm
6cm
5cm
3mm
7mm
6mm
9m
5m
5m
d
3m
4m
4m
4cm
a
6cm
40cm2
9m
5m
b
c
8mm
7mm
49m2
42mm2
35cm2 30mm2 35m2
14m2
8cm 7m 4mm
35cm
15cm
8cm
6cm
10cm
5cm 4cm
6cm
5cm
426cm2
Problem
Solving
The diagram shows the cross-section
of a wall of a cinema. It is to be
painted. Paint cost £6 for a tin which
covers 25m2. How much will it cost to
paint?
130m2
27m
2
64m2
221m2
£54