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