Measurement, NAPX-E4-CA26

Question

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Worked Solution

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Variant 0

DifficultyLevel

704

Question

A builder is tiling a floor that is 240 cm wide and 360 cm long.

She uses the triangular floor tile that is drawn below.



She uses all of her tiles and has no gaps between them.

How many tiles does she need?

Worked Solution

Strategy 1

2 tiles form a  4×12\ 4 × 12 cm  rectangle.

Fitting rectangles into floor plan:

Width = 2404\dfrac{240}{4} = 60 rectangles

Length = 36012\dfrac{360}{12} = 30 rectangles

∴\therefore Total tiles

= 2 × (30 × 60)

= 3600


Strategy 2
Area of 1 triangle = 12×4×12\dfrac{1}{2} \times 4 \times 12
= 24 cm2^2

∴\therefore Tiles needed = (240×360)÷24(240 \times 360) \div 24
= 3600

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A builder is tiling a floor that is 240 cm wide and 360 cm long. She uses the triangular floor tile that is drawn below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-E4-CA26.svg 240 indent vpad
She uses all of her tiles and has no gaps between them. How many tiles does she need?
workedSolution
Strategy 1 2 tiles form a $\ 4 × 12$ cm  rectangle. Fitting rectangles into floor plan: Width = $\dfrac{240}{4}$ = 60 rectangles Length = $\dfrac{360}{12}$ = 30 rectangles sm_nogap $\therefore$ Total tiles >>= 2 × (30 × 60) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 4 \times 12$ | | | = 24 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Tiles needed | = $(240 \times 360) \div 24$ | | | = {{{correctAnswer}}} |
correctAnswer
3600

Answers

Is Correct?Answer
x

900

x

1500

x

1800

✓

3600

Variant 1

DifficultyLevel

704

Question

A landscaper is tiling a patio that is 360 cm wide and 450 cm long.

He uses the triangular floor tile that is drawn below.



He uses all of his tiles and has no gaps between them.

How many tiles does he need?

Worked Solution

Strategy 1

2 tiles form a  12×5\ 12 × 5 cm  rectangle.

Fitting rectangles into floor plan:

Width = 36012\dfrac{360}{12} = 30 rectangles

Length = 4505\dfrac{450}{5} = 90 rectangles

∴\therefore Total tiles

= 2 × (30 × 90)

= 5400


Strategy 2
Area of 1 triangle = 12×12×5\dfrac{1}{2} \times 12 \times 5
= 30 cm2^2

∴\therefore Tiles needed = (360×450)÷30(360 \times 450) \div 30
= 5400

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A landscaper is tiling a patio that is 360 cm wide and 450 cm long. He uses the triangular floor tile that is drawn below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-CA26_5.svg 450 indent vpad
He uses all of his tiles and has no gaps between them. How many tiles does he need?
workedSolution
Strategy 1 2 tiles form a $\ 12 × 5$ cm  rectangle. Fitting rectangles into floor plan: Width = $\dfrac{360}{12}$ = 30 rectangles Length = $\dfrac{450}{5}$ = 90 rectangles sm_nogap $\therefore$ Total tiles >>= 2 × (30 × 90) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 12 \times 5$ | | | = 30 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Tiles needed | = $(360 \times 450) \div 30$ | | | = {{{correctAnswer}}} |
correctAnswer
5400

Answers

Is Correct?Answer
✓

5400

x

2700

x

1350

x

337.5

Variant 2

DifficultyLevel

703

Question

A pastry chef is cutting pastries from a sheet of pastry that is 96 cm wide and 55 cm long.

He cuts out pastry triangles in the shape shown below.



He uses the whole pastry sheet and has no pieces left over.

How many pastry triangles does he cut?

Worked Solution

Strategy 1

2 pastries form a  6×5\ 6 × 5 cm  rectangle.

Cutting pastries from the pastry sheet:

Width = 966\dfrac{96}{6} = 16 rectangles

Length = 555\dfrac{55}{5} = 11 rectangles

∴\therefore Total pastries

= 2 × (16 × 11)

= 352


Strategy 2
Area of 1 triangle = 12×6×5\dfrac{1}{2} \times 6 \times 5
= 15 cm2^2

∴\therefore Pastries cut = (96×55)÷15(96 \times 55) \div 15
= 352

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A pastry chef is cutting pastries from a sheet of pastry that is 96 cm wide and 55 cm long. He cuts out pastry triangles in the shape shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-CA26_4.svg 270 indent3 vpad
He uses the whole pastry sheet and has no pieces left over. How many pastry triangles does he cut?
workedSolution
Strategy 1 2 pastries form a $\ 6 × 5$ cm  rectangle. Cutting pastries from the pastry sheet: Width = $\dfrac{96}{6}$ = 16 rectangles Length = $\dfrac{55}{5}$ = 11 rectangles sm_nogap $\therefore$ Total pastries >>= 2 × (16 × 11) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 6 \times 5$ | | | = 15 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Pastries cut | = $(96 \times 55) \div 15$ | | | = {{{correctAnswer}}} |
correctAnswer
352

Answers

Is Correct?Answer
x

176

✓

352

x

480

x

960

Variant 3

DifficultyLevel

701

Question

Jeff is tiling his bathroom that is 2.4 m wide and 2.1 m long.

He uses the triangular floor tile that is drawn below.



He uses all of his tiles and has no gaps between them.

How many tiles does he need?

Worked Solution

Strategy 1

2 tiles form a  8×3\ 8 × 3 cm  rectangle.

Fitting tiles into floor plan:

Width = 2408\dfrac{240}{8} = 30 rectangles

Length = 2103\dfrac{210}{3} = 70 rectangles

∴\therefore Total tiles

= 2 × (30 × 70)

= 4200


Strategy 2
Area of 1 triangle = 12×8×3\dfrac{1}{2} \times 8 \times 3
= 12 cm2^2

∴\therefore Tiles needed = (240×210)÷12(240 \times 210) \div 12
= 4200

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Jeff is tiling his bathroom that is 2.4 m wide and 2.1 m long. He uses the triangular floor tile that is drawn below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-CA26_3.svg 270 indent vpad
He uses all of his tiles and has no gaps between them. How many tiles does he need?
workedSolution
Strategy 1 2 tiles form a $\ 8 × 3$ cm  rectangle. Fitting tiles into floor plan: Width = $\dfrac{240}{8}$ = 30 rectangles Length = $\dfrac{210}{3}$ = 70 rectangles sm_nogap $\therefore$ Total tiles >>= 2 × (30 × 70) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 8 \times 3$ | | | = 12 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Tiles needed | = $(240 \times 210) \div 12$ | | | = {{{correctAnswer}}} |
correctAnswer
4200

Answers

Is Correct?Answer
x

91

x

2100

✓

4200

x

4582

Variant 4

DifficultyLevel

700

Question

Carmen is cutting material for a patchwork quilt. The finished quilt will measure 180 cm wide and 196 cm long.

She uses the triangular template that is drawn below.



She covers the area exactly and has no gaps between the pieces.

How many triangular pieces does she need?

Worked Solution

Strategy 1

2 triangles form a  12×7\ 12 × 7 cm  rectangle.

Fitting triangles into quilt measurements:

Width = 18012\dfrac{180}{12} = 15 rectangles

Length = 1967\dfrac{196}{7} = 28 rectangles

∴\therefore Total tiles

= 2 × (15 × 28)

= 840


Strategy 2
Area of 1 triangle = 12×12×7\dfrac{1}{2} \times 12 \times 7
= 42 cm2^2

∴\therefore Tiles needed = (180×196)÷42(180 \times 196) \div 42
= 840

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Carmen is cutting material for a patchwork quilt. The finished quilt will measure 180 cm wide and 196 cm long. She uses the triangular template that is drawn below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-CA26_2.svg 400 indent vpad
She covers the area exactly and has no gaps between the pieces. How many triangular pieces does she need?
workedSolution
Strategy 1 2 triangles form a $\ 12 × 7$ cm  rectangle. Fitting triangles into quilt measurements: Width = $\dfrac{180}{12}$ = 15 rectangles Length = $\dfrac{196}{7}$ = 28 rectangles sm_nogap $\therefore$ Total tiles >>= 2 × (15 × 28) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 12 \times 7$ | | | = 42 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Tiles needed | = $(180 \times 196) \div 42$ | | | = {{{correctAnswer}}} |
correctAnswer
840

Answers

Is Correct?Answer
x

420

✓

840

x

928

x

1857

Variant 5

DifficultyLevel

708

Question

Bernice is tiling a mural that is 330 cm wide and 450 cm high.

She uses the triangular wall tile that is drawn below.



She uses all of her tiles and has no gaps between them.

How many tiles does she need?

Worked Solution

Strategy 1

2 tiles form a  15×5\ 15 × 5 cm  rectangle.

Fitting tiles into floor plan:

Width = 33015\dfrac{330}{15} = 22 rectangles

Length = 4505\dfrac{450}{5} = 90 rectangles

∴\therefore Total tiles

= 2 × (22 × 90)

= 3960


Strategy 2
Area of 1 triangle = 12×15×5\dfrac{1}{2} \times 15 \times 5
= 37.5 cm2^2

∴\therefore Tiles needed = (330×450)÷37.5(330 \times 450) \div 37.5
= 3960

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Bernice is tiling a mural that is 330 cm wide and 450 cm high. She uses the triangular wall tile that is drawn below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX-E4-CA26_1.svg 400 indent vpad
She uses all of her tiles and has no gaps between them. How many tiles does she need?
workedSolution
Strategy 1 2 tiles form a $\ 15 × 5$ cm  rectangle. Fitting tiles into floor plan: Width = $\dfrac{330}{15}$ = 22 rectangles Length = $\dfrac{450}{5}$ = 90 rectangles sm_nogap $\therefore$ Total tiles >>= 2 × (22 × 90) >>= {{{correctAnswer}}}
Strategy 2
| | | | --------------------- | -------------------------------------------- | | Area of 1 triangle | = $\dfrac{1}{2} \times 15 \times 5$ | | | = 37.5 cm$^2$|

| | | | --------------------- | -------------------------------------------- | | $\therefore$ Tiles needed | = $(330 \times 450) \div 37.5$ | | | = {{{correctAnswer}}} |
correctAnswer
3960

Answers

Is Correct?Answer
x

1980

x

2475

✓

3960

x

4950

Tags

  • ms_ca