area and perimeter (advanced) - squarespace · title: area and perimeter (advanced) author: mikal...

Mathematics - Topic 21 - Area and Perimeter (advanced)

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6

The square below is made up of 4 equal segments. The area of one segment is 25cm2. Find the perimeter of the whole square.

1

2 Sevak has some rectangular tiles. Each tiles is 7cm x 3cm. He makes a design with them. Calculate the height and width of the design.

cm

cmHeight

Width

cm

a

b

Calculate the perimeter of his design.

cm 1

1

Perimeter

Sevak also has some square tiles measuring 2cm x 2cm. He uses them to make a new design. Work out the length labelled x.

2cm

2cm

cmLength of x

25cm2

Height

Width

7cm

3cm

x

7cm

3cm

Working

Working

Section A: Short Questions

i

ii


A square with perimeter 4y is cut in half to make two identical rectangles.3

a Circle the correct expression for the perimeter of one rectangle

3y 2y 4y 2.5y 3.5y

c Circle the correct expression for the area of one rectangle.

3y2 4y2 2y2 0.5y2 1.5y2

1

1

18cm

The shape below is made up of five identical squares.

Calculate the perimeter of the shape.

Calculate the area of the shape.

a

b

cm

cm2

The following shape is made up of two types of triangles. The dimensions of the triangles are shown below. Calculate the perimeter of the shape.

10cm

7.5cm

12.5cm

6cm

8cm 10cm

4

5

1

1

cm

Working

3

7


6 The area of the white rectangle is 74cm2

a Work out the area of the grey triangle.

Working

b The same rectangle is now split into quarters. Work out the area of the grey triangle.

Working

cm2

cm2

2

2

7 Pick the correct expression for the perimeter of the shape below.

2x

y

4x + 4y x + 3y

4x + 2y

2x + 2y

1

3x + 2y4x + y

8 Sam needs to buy a grey picture frame for a photo he took. The frame is shown below.

Calculate the area of the frame.

Working

cm23

8

8.5cm

14cm1cm

1cm

10.5cm

9


Work out the area of the following shapes.

a

b

11cm

9cm

13cm

m94 m9

7

m129

Working

cm2

cm2

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10 The length of a rectangle is 9.6 units. The perimeter of the rectangle is 26.8 units. Calculate the width of the rectangle.

1

2

9.6cm

width

cm

Working

2

11 Anam uses 3 shapes to make a trapezium. Work out the area of the trapezium.

8cm

12cm

3.5cm

cm22

7

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12


Paul has a rectangular garden that measures 12m by 9m. Paul wants to fertilise the garden. One bag of fertiliser can cover 18m2. Each bag of fertiliser costs £8.99. How much would it cost to fertilise the whole garden?

a

b Tarik's garden has a curved border around his lawn. The rest of the garden is tiled with grey brick. The area of the bricked part of the garden is 28m2. Using the information below, calculate the area of the lawn.

Working

£

cm2m

m

Lawn

7 31

2110

Working

2

2

Saakib needs to tile a floor. The tiles measure 15cm by 15cm. How many tiles are needed to tile the floor?

tiles

Working

3

7

13

0.6m0.9m

1.5m

30cm 30cm

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Look at the shape below. It is made up of three different shapes that form a square. The shapes are labelled A, B and C. M represents the midpoint of the square. The diagonal length of the square is 25m.

a

Working

2

3

5

What is the area of B plus the area of C?

b Calculate the area of C to the nearest whole number.

Working

m2

cm2

M A B

C

15m

15m

6.25m

End of Section A

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a Nazish and her family plan to travel to the beach. Nazish makes a kite (made out of two triangles) so that she can fly it when she arrives at the beach. She wants to know the area of the kite. However she doesn't know the lengths of every side. What she does know is that the height of the smaller triangle is half of the height of the bigger triangle and that the length of the kite is 24cm. She also knows that the area of the smaller triangle is 36cm2. Use this information to answer the following questions.

What is the height of the smaller triangle?

What is the area of the bigger triangle?

What is the area of the kite?

cm

cm2

4

3

cm22

24cm

9cm

36cm2

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ii

iii

Working

Working

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Section B: Long Questions


b Nazish and her family finally arrive at the beach. After playing with her kite, Nazish wants to lay the kite down on a rug. There are already two items on the rug that are taking up space. One of the items is a t-shirt and the other item is a flat chessboard. The area of the grey part of the t-shirt is 322cm2 and the length of each square on the chessboard is 1.5cm. These items are shown below.

cm 5

i

ii

What is the combined area of the t-shirt and chessboard?

30cm

17cm

5cm

Nazish places the kite on the rug. There is still 681cm2 of space left on the rug. If the width of the rug is 30cm, calculate the length of the rug.

6 cm2

Working

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11

2


Zain wants to tile the floor of his new swimming pool. The length of the pool is 60m and the width is 12.6m. Zain's local DIY store sells tiles in batches of 500. A batch of 500 tiles costs £240. Each tile is 120cm long and 70cm wide. Zain doesn't know how to tile the pool himself and so he hires a builder to do the work. The builder charges £0.20 for every 3 tiles laid. In addition to buying the tiles, Zain will also need to provide the builder with sand and cement. For every 250 tiles, the builder will need 1 bag of cement and 2 bags of sand. 1 bag of cement costs £12.99 and 1 bag of sand costs £18.35. Use this information to answer the following questions.

a

b

What is the area of the swimming pool in metres?

What is the area of the swimming pool in centimetres?

c How many tiles are needed to tile the swimming pool

Working

Working

Working

m2

cm2

tiles

2

2

2

6

12.6m

60m


d What is the cost of each tile bought from the DIY store?

Working

£ 1

e Given that Zain can only buy tiles in batches, and sand and cement in whole bags, how many bags of sand and cement are required to tile the swimming pool?

Working

f What is the total cost of sand and cement required?

g Given that Zain can only buy tiles in batches, and sand and cement in whole bags, what is the total cost of tiling the swimming pool (including all labour costs and materials)

Working

Working

2

£ 2

£ 3

10

Sand

Cement

2

3


h The local DIY store offers a deal to Zain. A batch of 500 tiles still costs £240. However, the next 100 tiles bought will cost £0.30 per tile and any tiles bought after that will cost £0.26 per tile. Zain can still only buy sand and cement in whole bags. Calculate the new cost of building the wall (including all labour costs and materials

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£ 4

4

A magazine has 68 pages. Each page consists of pictures, text and advertisements. Each page is 30cm by 16cm, of which 50% is covered by pictures, 25% covered by text and 25% covered by advertisements. 20 words take up 8cm by 2cm of space. Each page also has 3 advertisements. There is 1 large, 1 medium and 1 small advertisement per page. A large advertisement measures 15cm by 4cm and is triple the size of a small advertisement. Use this information to answer the following questions.

Pictures

Adve

rtism

ents

30cm

16cm


a Given that text takes up 25% of each page of the magazine, how many words can be fit on a page?

Working

4

5

11

b Given that text takes up 25% of each page of the magazine, how many words can be fit in the whole of the magazine?

Working

2

c Work out the area of a medium advertisement.

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cm2


d

One of the pages has 5 identical pictures. What is the area of each picture?

Working

cm24

2

9

The width of each of the 5 pictures is 6cm. What is the length of each of the 5 identical pictures?

cm

Working

3

c If each page was cut out of the magazine and laid out side by side, what would be the total area of all the pages?

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cm2

i

ii

End of Section B

Total 100

area and perimeter (advanced) - squarespace · title: area and perimeter (advanced) author: mikal...

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