Perimeter & Area
Area of Shapes• The area of a shape is the space it occupies.• Try guessing the name of these shapes first:
Square
Rectangle
Parallelogram Trapezium
CircleTriangle
The Square Area = l x b
l
b
e.g. Find the area of a square of side 3.5 cm.
Discuss and work outthis example
together with your friend.
A = l x b
A = 3.5 cm x 3.5 cm
= 12.25 cm2
The Rectangle Area = l x b
l
b
e.g. Find the area of a rectangle of length 3.5 cm and height 80 mm.
Discuss and work outthis example
together.
Since units must be the same:10 mm = 1 cm80 mm = 80 mm ÷ 10 = 8 cm
A = l x bA = 3.5 cm x 8 cm
= 28 cm2
The Parallellogram Area = b x h
baseb
heighth
b
h
e.g. Find the area of a parallelogram correct to 1 d.p.
3.8 cm
10.3 cm
Discuss and work outthis example
together.
A = b x hA = 10.3 cm x 3.8 cm
= 39.14 cm2
= 39.1 cm2
The Triangle Area = ½ b h e.g. Find the area of triangle ABC
correct to the nearest cm2.
Discuss and work outthis example
together.
A = ½b x hA = ½ x 4 cm x 11.7 cm
= 23.4 cm2
= 23 cm2
baseb
heighth
Area of parallelogram = b hb
h
Area of = ½ area of parallelogram b
h
11.7 cm
4 cm
A
B C
Area of = ½b h b
h
b Area of trapezium = ½ h(a + b)Rotate the trapeziumThe 2 trapeziums form a parallelogram Area of parallelogram = h(a + b) Area of 1 trapezium is half h(a + b)
Area = ½h(a + b)a
b
h
h
a
e.g. Find the area of the trapezium.
12 cm
8.5 cm
6 cm
Decide about the values of a, b and h
to find the area.
h = 6cm, a = 8.5 cm, b = 12 cm
A = ½h(a + b)
A = ½ x 6 cm x (8.5 cm + 12 cm)= ½ x 6 cm x 20.5 cm = 61.5 cm2
The Trapezium
Length of side a
Length of side b
Copy the trapeziuma
b
height
The Circle Area = r2
CentreRadiusr
Remember: the radius
of a circle is half the diameter.
e.g. The diameter of a circle is 19 cm. Find, correct to nearest whole number, the area of a circle.
Find the radius first and then work out
this example together.
r = 19 cm ÷ 2= 9.5 cm.
A = r2
= x 9.5 cm x 9.5 cm= 283.5 cm2
= 284 cm2
Answers:
6a) $1.92
6b) $2.70
6c) $3.08
6d) $1.00
6e) H
Find the perimeters of the following:
Find the perimeter of the following:
Areas:
• Defines the size of an enclosed space, by calculating the number of square units of a certain size which are needed to cover the surface of a figure. Hence why area is measured in units squared.
• E.g. the area of the shape below is 8 units2
Areas of plane shapes:
Answers:
• 9) 10.65 cm2
• 10) 26.46 cm2
• 11) 55 m2
• 12) 15 m2
• 13) 3.64 m (2dp)• 14) roses = 16 m2, azaleas 28 m2, vegetables =
40 m2, total = 84 m2
• 15a ) i) 1867.6 m2, ii) 1395 m2, iii) 1215 m2, iv) 1750m2
• 15b) Trapezium, c) i)6227.5 m2, d) ii) 0.62275 ha
Proof of Area rule of a Trapezium
Start with Trapezium of height h, with lengths a and b
Split trapezium up into 2 triangles and 1 rectangle.
Find the area of the individual components.
Find the area of the following trapezium.
Find the ratio
• Draw 5 – 10 circles, starting off with circles with a small radius, moving up to those with a larger radius.
• Measure the circumference (piece of string?) and diameter of each circle.
• Find the ratio between the circumference and diameter of a circle.
StarterQ1) Q2)
a)b)
c)
d)
answers
• 1) 25m2 larger
• 2a) 50m2
• 2b) 5cm, because it is the depth
• 3c) 1700
Starter
• 1300