NORTHERN CAPE DEPARTMENT OF EDUCATION

MATHEMATICAL

LITERACY

LEARNER NOTES

PERIMETER, AREA AND

SURFACE AREA

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PERIMETER, AREA AND SURFACE AREA

Check that all measurements are in the same units, otherwise first convert all units into

those specified by the question, before doing calculations.

PERIMETER

The border or outer boundary lengths of a two-dimensional figure.

The perimeter of a circle is known as a circumference.

Since perimeter has to do with lengths, the units of perimeter are mm, cm, m or km.

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AREA

The surface enclosed by the boundary lengths of a two-dimensional figure.

Since area is the product of two-dimensional lengths, the units of area are mm², cm², m²

or km².

TOTAL SURFACE AREA

The total exterior area of all the exposed surfaces of a three dimensional object.

The only difference between total surface area (TSA) and area, is that TSA refers to 3-D

objects, while area refers to 2-D objects.

Since TSA is the sum of all the areas, the units of TSA are mm², cm², m², or km².

Rectangular prism = (2 × length × breadth) + (2 × length × height) + (2 × breadth × height)

Cylinder = [2 × π × (radius)²] + [2 × π × (radius) × height] where π = 3,142

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QUESTION 1

Jolandi decides to make place mats from wooden planks for each guest at her wedding

reception. She has 125 guests (including the bride and groom). The place mats are

rectangular, as indicated in the diagram below.

Each place mat consists of 2 vertical wooden planks onto which 6 horizontal planks are

attached. Each plank is 30 mm wide and 5 mm thick.

PHOTO OF PLACE MAT

DIAGRAM OF PLACE MAT

[Adapted from: www.pinterest.com]

Use the information above and answer the questions that follow.

1.1 Calculate the total area that will be covered by one place mat.

You may use the following formula:

Area of rectangle = length × width

(2)

1.2 To make one place mat, each plank is varnished individually on the front and

back before it is attached.

Varnish are sold in 1 litre cans. An area of 12 m² can be covered by one can of

varnish.

Calculate how many cans of varnish Jolandi will need to varnish all the place

mats for all the guests.

(7)

30,5 cm

23 cm

30 mm

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QUESTION 2

2.1 Liam and Amy are planning their wedding. Amy wants a four-layer red velvet

wedding cake. She must still decide between a cylindrical or rectangular cake as

shown on ANNEXURE A.

Use ANNEXURE A to answer the questions that follow.

2.1.1 Determine the total height of the cylindrical cake in millimetres. (3)

2.1.2 The base (bottom) layer of the cylindrical cake has a radius of 14

cm.

Determine the diameter of the base layer in cm.

(2)

2.1.3 Define the term perimeter. (2)

2.1.4 Calculate the area (in cm2) of the base of the pan needed to bake the

top layer of the rectangular cake.

You may use the following formula:

Area = length × width

(2)

2.2 Aunt Abby will bake the wedding cake. She will be using a recipe from a recipe

book published in England.

NOTE:

1 kg = 2,25 pounds

1 mℓ flour = 0,7 g flour

2.2.1 Aunt Abby needs 3 and a half pounds of butter.

Determine the mass of butter, in kilogram.

(2)

2.2.2 Aunt Abby only has a kitchen scale available.

If aunt Abby needs 625 mℓ of flour, determine the mass of the flour

in grams.

(2)

2.2.3 The cake must be baked at 356 °F.

Determine to what degree Celsius the oven should be turned.

You may use the following formula:

°C = (°F – 32°) ÷ 1,8

(2)

[15]

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ANNEXURE A

QUESTION 2.1

FOUR-LAYER RED VELVET WEDDING CAKES

AMY'S FOUR-LAYER CYLINDRICAL RED VELVET WEDDING CAKE

height = h

AMY'S FOUR-LAYER RECTANGULAR RED VELVET WEDDING CAKE

35 cm

Length of top layer = 15 cm

Length of bottom layer = 35 cm

Width of top layer = 12 cm

Width of bottom layer = 33 cm

[Adapted from www.pinterest.com]

15 cm

Top layer

Base

(bottom)

layer

33 cm

12 cm

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QUESTION 3

Petru makes craft products that she sells at a craft market. She makes gift stockings (gift bags

shaped like a sock) decorated with triangular shapes, as shown below. She sews three

triangles onto each side of the stocking.

Photograph of a gift

stocking

Dimensions of the

triangular pieces of

fabric

Dimensions of a

rectangular piece of

fabric required for one

side of a stocking

[www.marthastewart.com]

3.1 The area of one side of a stocking (without the triangular pieces) is 355,25 cm².

Calculate the area of the fabric that is left over if Petru cuts ONE complete

stocking from two rectangular pieces of fabric.

You may use the following formula:

Area of rectangle = length × width

(6)

3.2 Calculate the total area of the triangular shapes needed to decorate ONE

stocking.

You may use the following formula:

Area of triangle = 2

1× base × height

(4)

3.3 It takes Petru 18 minutes to cut, decorate and hand-stitch one stocking.

Determine at what time she will finish making NINE stockings if she starts at

08:25.

(4)

[14]

5 cm

3 cm

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QUESTION 4

Below is a photograph of a glass ornament that Petru makes using 250 mℓ cylindrical glass

jars.

The inside radius of the glass jar is 3,25 cm.

The outside diameter of the lid of the jar is 72 mm and the height (h) is 9 mm.

The exterior surface of the lid is painted red.

The jar is filled 75% with water and a pinch of glitter is added to the water. A dash of

glycerine is also added to keep the glitter from sinking too quickly.

The figure is glued to the inside of the lid before the lid is placed on the jar. The jar is then

turned upside down.

4.1 Calculate (to the nearest cm²) the exterior surface area of the lid that needs to be

painted.

You may use the following formula:

Painted exterior surface area of lid = 2h) (r πr where 𝝅 = 3,142; r is the radius and h is the height of the lid.

(4)

4.2 Use the conversions below to answer the following questions.

1 pinch = 16

1

teaspoon

2 pinches = 1 dash

1 teaspoon = 5 mℓ

Determine what fraction of a teaspoon equals ONE dash.

(2)

[06]

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QUESTION 5

5.1 Justin has an injury that requires him to use a wheelchair for a while. He uses the

diagrams below to determine certain dimensions of the wheelchair.

Side view of the wheelchair Front view of the wheelchair

[Source: 1800wheelchair.com]

Use the diagrams above to answer the following questions.

5.1.1 The outer diameter of the bigger wheel is 54% of the length of the

wheelchair.

Determine the length of the outer diameter (rounded off to the

nearest mm) of the big wheel.

(4)

5.1.2 The big wheel has 24 equally

spaced cylindrical spokes

attached to the rim, as shown

in the picture alongside.

The diameter of each spoke

is 2 mm.

The inner diameter of the rim

is 584 mm.

Calculate how far apart the wheel spokes are spaced from each other on

the rim.

You may use the following formula:

Circumference of a circle = π × diameter using π = 3,142

(6)

5.1.3 One of the doorway openings in Justin's house is 750 mm wide.

Determine, showing ALL calculations, how wide (in mm) the available

gap on both sides of the wheelchair is if the wheelchair passes through the

doorway opening exactly in the middle.

(4)

Width

Length

Big wheel

121,92 cm 60,96 cm

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5.2 The doorway of a museum is shown in the photograph and diagram below. It has two

identical doors that can open to allow for the easy flow of people.

The doors have glass-panel inserts, in the shape of rectangles and quarter circles,

embedded in a wooden frame, as shown in the photograph and diagram below.

The following formulae may be used:

Area of a rectangle = length × width

Area of a circle = π × (radius)2 using π = 3,142

Use the diagram above to answer the following questions.

5.2.1 Determine the total width, in metres, of the two doors. (3)

5.2.2 Calculate the value of e, the length of the rectangular glass-panel inserts. (4)

5.2.3 Calculate the total area (in mm2) of ALL the glass-panel inserts. (6)

[27]

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QUESTION 6

6.1 Confidence was interested in the amount of hours that she spend sleeping and the quality of

sleep. She tracked her sleeping pattern for seven (7) days using the fitness monitor watch.

TABLE 4: SLEEPING PATTERN TIMES IN HOURS AND MINUTES

Day Total Sleep Restful Sleep % Restless Sleep %

Monday 5h28min K 86 0h45min 14

Tuesday 7h16min 6h27min 89 0h49min 11

Wednesday 6h57min 5h57min 86 1h0min 15

Thursday 5h45min 5h33min 97 1h12min 3

Friday 7h11min 5h41min 79 1h30min 21

Saturday 8h39min 6h35min 76 2h04min 24

Sunday 8h35min 6h17min 73 2h18min 27

[Source: www.androidcentral.com]

NOTE: The minimum recommended total sleeping time for an adult is 7 hours per day.

6.1.1 Write down the restless sleeping time (in minutes) for Saturday. (2)

6.1.2 Name the day(s) on which Confidence exceeded the minimum recommended

sleeping time by LESS than 20 minutes.

(2)

6.1.3 Convert the time 6 hours 27 min to hours. (3)

6.1.4 Calculate K, the restful sleeping time (in hours and minutes) for Monday. (3)

6.1.5 Express the total sleeping time for Wednesday as a decimal of a day. (3)

6.1.6 Show that the total sleeping time from Monday to Sunday was 49h 51min. (3)

6.2 During the Idols South Africa music competition performances, contestants are allowed to

use the cylindrical stage as shown on ANNEXURE B. The diameter of the stage is

5 m and the height is 1,2 m.

6.2.1 Determine the radius of the stage. (2)

6.2.2 Calculate the area (to the nearest m²) of the stage. (3)

6.2.3 The manager wants to paint the sides of the stage with a special paint.

(a) Calculate the surface area of the sides of the stage. (2)

(b) The paint is sold in 1ℓ cans. Determine the number of 1ℓ cans of paint

that must be bought if a litre of paint covers an area of

2,4 m2.

(3)

[26]

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ANNEXURE B

QUESTION 6.2

Idols South Africa music competition cylindrical stage.

The following formulae may be used:

Area circle = 𝝅 × r2

Lateral Surface Area of right circular cylinder = 𝟐 × 𝛑 × 𝐫 × 𝐡

NOTE: r = radius h = height and 𝛑 = 3,142

5 m

1,2 m