Functional Skills Maths - · PDF file07.11.2016 · FS MATHS L2 – 7A V1.0 ... A rectangular patio is 2.5 m long and 180 cm wide. ... Give your answer to 1 decimal place

Maths Functional Skills

Level 2 Find area and perimeter of common shapes

v1.0

FS MATHS L2 – 7A V1.0

www.bksb.co.uk 2

Functional Skills Maths: Level 2 Skill Standard: 7a Coverage and Range: Find area, perimeter and volume of common shapes.

Know what is meant by perimeter, circumference, diameter and radius.

Understand and use given formulae for finding perimeters and areas of common and composite shapes, circumference and area of circular surfaces, for example rooms or plots of land.

Understand the symbol for pi and know its approximate value.

Understand and use given formulae for finding volumes of common shapes, for example cuboid or cylinder.

Know that measurements must be in the same units when calculating perimeters, areas and volumes.1

1 QCA Functional Skills guidance: amplification of the standards June 2008 QCA/08/3700


www.bksb.co.uk 3

Explain the Skill Perimeter The perimeter is the distance all the way around the edge of a shape. To calculate the perimeter, measure all the sides and add these measurements together. All the units must be the same. A rectangular patio is 2.5 m long and 180 cm wide. Calculate its perimeter in metres. Perimeter = 2 m + 2 m + 1.8 m + 1.8 m = 7.6 m You can also find the perimeter of a rectangle using a formula. The formula for a rectangle using P for the perimeter, l for the length and w for the width is: P = 2 l + 2w or P = 2( l + w)

w

l

2 m

180 cm


www.bksb.co.uk 4

What is the perimeter of the triangle shown below? Perimeter = 1.8 m + 6.5 m + 5.9 m = 14.2 m A composite shape is one that is made of two or more joined shapes. Its perimeter is found by adding the lengths of all the outside edges. What is the perimeter of the garden shown in the diagram? P = 33 m + 18 m + 16 m + 11 m + 15 m + 28 m P = 121 m The perimeter of the garden is 121 metres.

28 m

15 m

33 m

18 m

11 m

16 m

180 c

m

5.9 m


www.bksb.co.uk 5

If there are any lengths missing from the diagram, you need to work these out before calculating the perimeter. What is the perimeter of Alana’s room shown in the diagram? Work out the lengths of the sides not given in the question, then add together the measurements for all the sides. There is one missing measurement to calculate. The total length of the room is 5 m, take away the length opposite of 3.5 m. So the missing length = 1.5 m. Now simply add together the measurements for all the sides. 5 m + 1.5 m + 1.5 m + 1.5 m + 3.5 m + 3 m = 16 m

3.5 m

5 m

1.5 m

1.5 m

3 m

3.5 m

5 m

1.5 m

1.5 m

3 m

1.5 m


www.bksb.co.uk 6

Practise the Skill 1) An office is available to let and is advertised in a brochure. The dimensions are

shown below. What is the perimeter of the office?

_______ m

2) Calculate the perimeter of the Accounts Department shown below.

_______ m


www.bksb.co.uk 7

3) In the Accounts Department there is a storage area with the following dimensions.

What is the perimeter of the cupboard?

_______ m

4) What is the perimeter of the patio in the diagram below? ________ m


www.bksb.co.uk 8

5) Bill is looking at the plans for his new house.

Calculate the perimeter of his house. ________ m

6) The perimeter of a plot of land for a new housing development is 270 m. The width

of the site is 60 m.

What is the length of the building site? _______ m

7) Lisa’s kitchen is 6.5 m wide and the perimeter is 29.6 m.

What is the length of the kitchen? _______ m


www.bksb.co.uk 9

Explain the Skill Circumference The circumference is the distance all the way around the edge of a circle. The circumference is just like the perimeter but is only used when talking about circles. To calculate the circumference of a circle there are two formulae we can use.

Circumference = pi x diameter or C = πd The symbol used for pi is π π is approximately equal to 3.14

or

Circumference = 2 × pi × radius or C = 2πr The diameter of a circle is the distance across the centre. The diameter is the widest part of the circle.

The radius of a circle is the distance from the middle of the circle to the outside edge. The radius is exactly half of the diameter.


www.bksb.co.uk 10

Examples Unless otherwise stated use π = 3.14 Find the circumference of the circle shown below. C = πd π = 3.14 d = 6 cm C = 3.14 × 6 = 18.84 Circumference = 18.84 cm

Find the circumference of the circle shown below. C = 2πr π = 3.14 r = 5 cm C = 2 × 3.14 × 5 C = 31.4 Circumference = 31.4 cm


www.bksb.co.uk 11

Find the perimeter of the semicircle shown below. The perimeter of a semicircle is found by calculating the curved part which is half a circle plus the diameter line across the bottom. Perimeter of semicircle = πd + d 2 P = 3.14 x 4.6 + 4.6 2 P = 11.822 Perimeter = 11.8 m (to 1 d.p.)


www.bksb.co.uk 12

Practise the Skill 1) Formula for the circumference of a circle is: C = πd Pat has baked a cake and is going to decorate around the edge.

What is the circumference of the cake? ________ cm

2) A circular table has a radius of 55 cm.

What is the circumference of the table? ______ cm


www.bksb.co.uk 13

3) A big wheel at a theme park has a diameter of 135 m. What is the circumference of the big wheel?

_______ m 4) A circular mirror with a diameter of 60 cm has border around it of 8 cm.

What is the circumference of the border?

___________


www.bksb.co.uk 14

5) A semicircular pond has a diameter of 5.2 m.

What is the length of the outside edge of the pond? Give your answer to 1 decimal place.

_______ m 6) Steve is a member of the athletics club and trains twice a week. These are the

dimensions of the track he uses.

What is the perimeter of the running track?

_______ m


www.bksb.co.uk 15

Explain the Skill Area The area of a shape is a measure of the surface covered by a given shape. Area is measured in square units e.g. square millimetres (mm²) square centimetres (cm²) square metres (m²) square kilometres (km²). Remember that all measurements should be in the same units when calculating the area. The area of a rectangle is calculated by multiplying the length by the width. To calculate the area of a rectangle we use the formula: A = l x w Rectangle Calculate the area of this rectangle. Area of a rectangle = length x width A = 12.5 cm x 80 mm A = 12.5 cm x 8 cm A = 100 cm²


www.bksb.co.uk 16

Triangle The area of a triangle is half the area of a rectangle. To calculate the area of a triangle we use the formula: Area of a triangle = base × height 2 A = b × h 2 Calculate the area of this triangle. Area of a triangle = base × height 2 A = 9 cm x 50 mm 2 A = 9 cm x 5 cm 5 A = 22.5 cm


www.bksb.co.uk 17

Circle To calculate the area of a circle we use the formula: Area of a circle = π × (radius)2 A = πr2 Calculate the area of this circle. Use π = 3.14

Area of a circle = π × (radius)2

A = 3.14 x 52 cm A = 78.5 cm2


www.bksb.co.uk 18

Semicircle The area of a semicircle is half the area of a circle. To calculate the area of a semicircle we use the formula: Area of a semicircle = π × (radius)2 2 A = πr2 2 Calculate the area of this semicircle. Area of a semicircle = π × (radius)2

2 A = 3.14 x 82 2 A = 100.48 cm2


www.bksb.co.uk 19

Composite Shape A composite shape is one that is made of two or more joined shapes. To calculate the area of a composite shape you will need to split it up into separate, regular shapes. The area of each regular shape is calculated and all the areas are added together to find the total area. It is often possible to split the composite shape in several different ways. You choose the way that is easiest for you.

The shape is split into the two regular shapes A and B. Area of shape A = 8 × 7 = 56 cm2

Area of shape B = 5 × 3 = 15 cm2

Total area = 56 + 15 = 71 cm2

A

B

12 cm

5 cm

8 cm

7 cm


www.bksb.co.uk 20

Practise the Skill 1) Calculate the area of the garden below.

_______ m2

2) This is a diagram of a greenhouse. What is the area of the greenhouse?

_______ m²


www.bksb.co.uk 21

3) A semicircular pond has a diameter of 5.2 m. Use π = 3.14.

Area of a semicircle = π × (radius)2

2 What is the area of the pond? Give your answer to 1 decimal place.

_______ m2

4) What is the area of the grass section in the centre of the running track?

Use π= 3.14. Area of a semicircle = π × (radius)2 2

The area of the grass = __________ m2

Round your answer to 2 decimal places.


www.bksb.co.uk 22

5) The area of a room is 153 m². The width is 9 m.

What is the length of the room?

_______ m 6) Jasmine is going to treat the decking in her garden with preservative. The diagram

shows the area to be treated.

A tin of preservative covers 8 m².

How many tins of preservative will Jasmine need?

______ tins 7) The diagram shows the plan of a kitchen worktop. The worktop will be covered with

square tiles measuring 40 cm x 40 cm. How many tiles are needed to cover the worktop?

________

4 m

2 m

1.2 m

1.2 m

Documents

Functional Skills Maths - · PDF file07.11.2016 · FS MATHS L2 – 7A V1.0 ... A rectangular patio is 2.5 m long and 180 cm wide. ... Give your answer to 1 decimal place