Perimeter
Area of a rectangle
Area of
A Right-Angled Triangle
Composite Areas
Parallelogram Area
Rhombus Area
Trapezium Area
Starter Questions
1.
2.3 x 8
2.
Convert metres (m)
(a) 200 cm
3.
4.
(b) 550 cm
(c) 50 cm
3
of 320
4
Find 2 numbers that add to give 7
and multiply to give 10.
Starter Questions
Q1.
Estimate
(15  12)  14  10
Q2.
Round to the 2 decimal places.
(a)
Q3.
234.565 (b)
0.295
(c)
34.449
Round 2 significant figure.
(a)
345
(b)
1573
(c)
0.04567
Area
Base
Perimeter
Triangle
Length
Vocabulary
Widths
Height
Rectangular
Square
Perimeter
Perimeter
Perimeter
Perimeter
Perimeter
6cm
3cm
Perimeter =
Calculate the
perimeter of the
rectangle below.
6 + 3 + 6 + 3 = 18cm
Perimeter
3cm
4cm
Perimeter = 3 + 5 + 4 = 12cm
Perimeter
10cm
Calculate the perimeter
of the rectangle.
Perimeter = 28cm
4cm
Perimeter
Calculate the perimeter
12cm
5cm
of the triangle below.
Perimeter = 30cm
Area
Area
Base
Perimeter
Triangle
Length
Vocabulary
Widths
Height
Rectangular
Square
1m
1m
Problem…
= 1 square metre
6m
6 square metres
3m
6 square metres
6 square metres
3 rows of 6 squares = 3 x 6 = 18 square metres
Area of a rectangle
6length
6m
3
3m
breadth
6 x 3 = 18 m²
Area = length x breadth
Example 1
11 cm
6 cm
Find the area of
the rectangle
Area = length x breadth
A=lxb
A = 11 x 6
A = 66 cm²
Example 2
Area = length x breadth
A=lxb
A = 12 x 12
A = 144 cm²
12 cm
Find the area of
the square
Area of a rectangle
Exercise
Of
worksheet
Area of a Rectangle
Example
Find the area of the rectangle opposite B = 2cm
L = 9cm
Area = Length x Breadth
A=LxB
A=9x2
2
A = 18 cm
Success Criteria
SC 1
SC 2
SC 3
Area of
A Right-Angled Triangle
Area of
A Right-Angled Triangle
Calculate the area of this shape
A=lxb
A = 10 x 8
8cm
A = 80cm2
10cm
Area of
A Right-Angled Triangle
1
Area= base × height
2
1
A= b×h
2
Vertical
Height
base
Area of triangle
Short cut
4 cm
height
base 7 cm
Area of triangle = ½ x 7 x 4 = ½ x 28 = 14 cm²
Area Δ = ½ x base x height
Area of
A Right-Angled Triangle
Calculate the area of this shape
1
A= ×b×h
2
1
A= ×6×12
2
12cm
A=36cm
2
6cm
Area of
A Right-Angled Triangle
Calculate the area of this shape
3cm
4cm
1
A= ×b×h
2
1
A= ×4×3
2
A=6cm
2
Example 1
Area Δ=½ x base x height
AΔ =½ x b x h
10 cm
15 cm
Find the area of
the triangle
AΔ = ½ x 15 x 10
AΔ = 75 cm²
Example 2
Area Δ=½ x base x height
8 cm
AΔ =½ x b x h
12 cm
Find the area of
the triangle
AΔ = ½ x 8 x 12
AΔ = 48 cm²
Any Triangle Area
h = vertical height
Sometimes
called the
altitude
h
b
1
Area  b  h
2
Any Triangle Area
Example 1 : Find the area of the triangle.
1
Area  b  h
2
6cm
8cm
1
Area   8  6
2
Area  24cm 2
Any Triangle Area
Example 3 : Find the area of the isosceles triangle.
1
Area  b  h
2
3cm
1
Area   8  3
2
Area  12cm 2
8cm
Any Triangle Area
Example 2 : Find the area of the triangle.
Altitude h outside triangle this time.
10cm
4cm
1
Area  b  h
2
1
Area   4  10
2
Area  20cm 2
Any Triangle Area
Exercise
Of
worksheet
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  12cm2
5cm
3cm
4cm
6cm
Triangle Area =
1
1
b  h   6  5  15cm2
2
2
Total Area = 15 + 12 = 27cm
2
Composite shapes
10 cm
6 cm
?
13 cm
?
3 cm
Composite shapes
10 cm
6 cm
(1)
6 cm
?
Area (1) = l x b = 10 x 6 = 60 cm²
(2)
3 cm
Area (2) = ½ x b x h = ½ x 3 x 6 = 9 cm²
Area of shape = (1) + (2) = 60 + 9 = 69 cm²
Composite shapes
Exercise
Of
worksheet
Quadrilateral Family
parallelogram
rectangle
trapezoid
rhombus
square
Copyright © 2000 by Monica Yuskaitis
Insert Lesson Title Here
Vocabulary
parallelogram
rhombus
rectangle
square
trapezoid
kite
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A rectangle has four right angles.
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A square has four congruent sides
and four right angles.
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A trapezoid has exactly one pair
of parallel sides.
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A kite has exactly two pairs of congruent
adjacent sides.
Additional Example 1A: Identifying Types
of Quadrilaterals
Give all the names that apply to the quadrilateral.
This figure has two pairs
of parallel sides, so it is
a parallelogram.
It has four congruent
sides, so it is also a
rhombus.
Additional Example 1B: Identifying Types of
Quadrilaterals
Give all the names that apply to the quadrilateral.
The figure has exactly two
pairs of congruent,
adjacent sides, so it is a
kite.
It does not fit the
definitions of any of the
other special quadrilaterals.
Try This: Example 1A
Give all the names that apply to the quadrilateral.
This figure has two pairs
of parallel sides, so it is
called a parallelogram.
It has four right angles,
so it is also a rectangle.
Try This: Example 1B
Give all the names that apply to the quadrilateral.
6 ft
6 ft
6 ft
6 ft
The figure has two pairs
of parallel sides, so it is
a parallelogram.
It has four congruent sides,
so it is also a rhombus.
Try This: Example 1C
Give all the names that apply to the quadrilateral.
The figure has exactly
one pair of parallel sides,
so it is a trapezoid.
It does not fit the
definitions of any of the
other special quadrilaterals.
Starter Questions
Q1.
Solve the equation below
x  21  32
a
o
Q2.
Find the missing angles
Q3.
Find the average of the numbers below
2,5,6,7
Q4.
Find
75% of £240
b
o
Simple Areas
Definition : Area is “ how much space a shape takes up”
A few types of special Areas
Any Type of Triangle
Rhombus and kite
Parallelogram
Trapezium
Any Triangle Area
h = vertical height
Sometimes
called the
altitude
h
b
1
Area  b  h
2
Any Triangle Area
Example 1 : Find the area of the triangle.
1
Area  b  h
2
6cm
8cm
1
Area   8  6
2
Area  24cm 2
Any Triangle Area
Example 2 : Find the area of the triangle.
Altitude h outside triangle this time. Area  1 b  h
2
10cm
4cm
1
Area   4  10
2
Area  20cm 2
Hint : Use
Pythagoras Theorem
first !
Any Triangle Area
Example 3 : Find the area of the isosceles triangle.
a 2  b2  c2
42  b 2  52
1
Area  b  h
2
5cm
b 2  52  42
b2  9
b  9
b 3
4cm
8cm
1
Area   8  3
2
Area  12cm 2
Starter Questions
Q1.
Find the area of the triangle.
3cm
Q2.
Expand out ( w - 5) (2w2 + 2w – 5)
Q3.
True or false
50.5 - 1.65  20 = 977
Q4.
Rearrange into the form y =
y – 3x + 7 = 0
10cm
4cm
Parallelogram Area
Important NOTE
h
h = vertical height
b
Parallelogram Area =b  h
Parallelogram Area
Example 1 : Find the area of parallelogram.
3cm
Parallelogram Area  b  h
9cm
Area = 9  3
2
Area = 27cm
Starter Questions
Q1.
True or false
Q2.
Does 2.5 + 1.25 x 20 = 27.55 Explain your answer
Q3.
Expand ( y - 3) (2y2 + 3y + 2)
Q4.
Calculate
2
b c2
3
2x2 – 72 = 2(x – 6)(x + 6)
, b = -18 c = -6
This part of
the rhombus
is half of the small
rectangle.
Area of a Rhombus
B
L
Rectangle Area = L ᵡ B
M at h Com poser 1. 1. 5
ht t p: / / www. m at hcom poser . com
Rhombus Area = 1 L ᵡ B
2
Area of a Kite
Exactly the same process as the rhombus
B
L
Rectangle Area = L ᵡ B
M at h Com poser 1. 1. 5
ht t p: / / www. m at hcom poser . com
Kite Area = 1 L ᵡ B
2
Rhombus and Kite Area
Example 1 : Find the area of the shapes.
2cm
5cm
9cm
M at h Com poser 1. 1. 5
ht t p: / / www. m at hcom poser . com
Rhombus Area = 1 L ᵡ B
2
1
Area = (5  2)
2
Area = 5cm2
4cm
M at h Com poser 1. 1. 5
ht t p: / / www. m at hcom poser . com
Kite Area = 1 L ᵡ B
2
1
Area = (9  4)
2
Area = 18cm
2
Rhombus and Kite Area
Example 2 : Find the area of the V – shape kite.
M at h Com poser 1. 1. 5
ht t p: / / www. m at hcom poser . com
Kite Area = 1 L ᵡ B
2
4cm
1
Area = (7  4)
2
7cm
Area = 14cm
2
Starter Questions
Q1.
Find the area of the parallelogram
7
7
Q2.
Solve the equation (ie find the root) to 1 dp
x2 + 4x – 3 = 0
Q3.
A can of beans is reduce by 15% to 25p.
Find the price before the reduction.
Q4.
The speed of light is 300000000 metres per sec.
True or false in scientific notation 3 x 108.
Trapezium Area
a cm
X
h cm
Two triangles WXY and WYZ
Y
1
Area 1 = a  h
2
1
1
bh
2
2
Total Area =
W
Area 2 =
b cm
Z
1
1
ah  bh
2
2
1
Trapezium Area = (a +b)h
2
Trapezium Area
Example 1 : Find the area of the trapezium.
5cm
4cm
1
Trapezium Area = (a  b)h
2
1
Trapezium Area = (5  6)  4
2
6cm
Trapezium Area = 22cm
2
Starter Questions
Q1.
9
8
Find the area of the trapezium
7
Q2.
Explain why the perimeter of the
shape is 25.24cm.
30o r = 10cm
Q3.
y varies directly as the square of x.
When y = 25 , x = 4
Find the value of y when x = 10
Composite Areas
Example 2 : Find the area of the shaded area.
8cm
11cm
4cm
10cm
Trapezium Area - Triangle Area
1
Trapezium Area = (a  b)  h
2
1
= (10  8) 11  99cm 2
2
1 = 1  4  11  22cm 2
Triangle Area = bh 2
2
Shaded Area = 99 - 22  77cm2
Summary Areas
Any Type of Triangle
1
Area  b  h
2
Parallelogram
Area  b  h
Rhombus and kite
1
Area  ( D
d)
B× L
2
Trapezium
1
Area = (a + b)h
2