Starter
MNU 2-11c
MTH 3-11a
MTH 3-11b
Find the area of these composite shapes:
3
1
2
Rhombus and Kite Area
Learning Intention
1.
To develop a single
formula for the area of
ANY rhombus and Kite.
Success Criteria
1. To remember the formula
for the area of ANY
rhombus and kite.
2. Apply formulae correctly.
(showing working)
3. Answer containing
appropriate units
MNU 2-11c
MTH 3-11a
MTH 3-11b
The Rhombus
Leaning square
A Rhombus is a 4-sided polygon
All 4 sides must be equal
In length
The opposite sides are parallel
The opposite inside angles are equal
Area of a Rhombus
D2
D1
Rectangle Area = Diagonal 1 x Diagonal 2
Rhombus Area:
1
𝐴 = × 𝐷1 × 𝐷2
2
Area of a Kite
D2
D1
Rectangle Area = D x d
Kite Area:
1
𝐴 = × 𝐷1 × 𝐷2
2
Rhombus and Kite Area
Example : Find the area of the shapes.
2cm
5cm
1
Rhombus Area  ( D  d )
2
1
Area = (5  2)
2
Area = 5cm
2
4cm
9cm
1
Kite Area  ( D  d )
2
1
Area = (9  4)
2
Area = 18cm
2
Rhombus and Kite Area
Example : Find the area of the V – shape kite.
1
Kite Area  ( D  d )
2
1
Area = (7  4)
2
4cm
7cm
Area = 14cm
2
MNU 2-11c
MTH 3-11a
MTH 3-11b
Starter Questions
Q1.
Is the area of the rhombus
equal to 10.5cm2
Explain your answer.
6cm
7cm
Q2.
Show that there are 2880 minutes in 2 days
Q3.
Expand 2p( y - 3p) – 2py
Q4.
Calculate
a (b  c )
a = -2 , b = -4 c = 6
Parallelogram Area
Learning Intention
1.
To develop a formula for
the area of a parallelogram.
Success Criteria
1. To remember the formula
for the area of a
parallelogram.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
Parallelogram Area
Important NOTE
h = vertical height
h
b
Parallelogram Area  b  h
Parallelogram Area
Example 1 : Find the area of parallelogram.
3cm
Parallelogram Area  b  h
9cm
Area = 9  3
Area = 27cm
2
Starter Questions
Q1.
Find the area of the parallelogram
8
7
Q2.
Is the HCF 6 and 24 24 Explain your answer.
Q3.
Show that 11.5 % of 150 is 17.25
Q4.
Simplify 3(h -2) + h(2 - 4h) = -4h2 + 6h - 6
Trapezium Area
Learning Intention
1.
To develop a formula for
the area of a trapezium.
Success Criteria
1. To remember the formula
for the area of a trapezium.
2. Apply formula correctly.
(showing working)
3. Answer containing
appropriate units
Trapezium Area
a cm
X
h cm
W
Two triangles WXY and WYZ
Y
1
Area1  ah
2
1
2
b cm
Z
1
Area2  bh
2
1
1
Total Area  ah  bh
2
2
1
Total Area  (a  b)h
2
Trapezium Area
Example : Find the area of the trapezium.
5cm
4cm
1
Area  (a  b)h
2
1
Trapezium Area = (5  6)  4
2
6cm
Trapezium Area = 22cm 2
Starter Questions
Q1.
Find the area of the trapezium
9
8
Q2.
Is the HCF for 4 and 12 equal to 2.
Explain your answer.
Q3.
Find 6.5% of 60
Q4.
Is
7
3(f – 4) - 4f = 7f -12 Explain your answer
Composite Areas
Learning Intention
1.
To show how we can apply
basic area formulae to solve
more complicated shapes.
Success Criteria
1. To understand the term
composite.
2. To apply basic formulae to
solve composite shapes.
3. Answer containing
appropriate units
Composite Areas
We can use our knowledge of the basic areas
to work out more complicated shapes.
Example 1 : Find the area of the arrow.
Rectangle Area = l  b  3  4  12cm 2
5cm
3cm
4cm
6cm
Triangle Area =
1
1
b  h   6  5  15cm 2
2
2
Total Area = 15+12=27cm 2
Composite Areas
Example : Find the area of the shaded area.
8cm
Trapezium Area - Triangle Area
Trapezium Area =
11cm
=
4cm
10cm
1
( a  b)  h
2
1
(10  8)  11  99cm 2
2
1
1
Triangle
=  4 Area
11  22
= cmbh2
2
2
Shaded Area = 99 - 22  77cm 2