Measurement, NAPX-I4-CA27 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

715

Question

A museum has a glass entrance that is made up of four equal triangles and a square, as shown in the diagram below.



Belou is hired to clean the interior sides of the entrance, not including the floor.

What is the area that Belou will need to clean? Answer to the nearest square metre.

Worked Solution

Area to clean
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 18 × 17.7
= 637.2 m²
= 637 m2^2 (nearest m²)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A museum has a glass entrance that is made up of four equal triangles and a square, as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA272.svg 440 indent vpad
Belou is hired to clean the interior sides of the entrance, not including the floor. What is the area that Belou will need to clean? Answer to the nearest square metre.
workedSolution
sm_nogap Area to clean
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 18 × 17.7| |= 637.2 m²| |= {{{correctAnswer0}}} {{{suffix0}}} (nearest m²)|
correctAnswer0
637
prefix0
suffix0
m$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0637

m2^2

Variant 1

DifficultyLevel

713

Question

A light fitting is made up of four equal triangles and a square, as shown in the diagram below



Chrissy is spray painting the outside of the light fitting, not including the base.

What is the area that Chrissy will need to paint?

Worked Solution

Area to paint
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 25 × 46
= 2300 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
A light fitting is made up of four equal triangles and a square, as shown in the diagram below
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-I4-CA27-SA_1.svg 450 indent vpad
Chrissy is spray painting the outside of the light fitting, not including the base. What is the area that Chrissy will need to paint?
workedSolution
sm_nogap Area to paint
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 25 × 46| |= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
2300
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer02300

cm2^2

Variant 2

DifficultyLevel

712

Question

A large glamping tent is made up of four equal triangles and a square, as shown in the diagram below



Bruce is covering the outside of the tent with waterproofing spray, not including the base.

What is the area that Bruce will need to spray? Answer to the nearest square metre.

Worked Solution

Area to spray
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 4.5 × 3.6
= 32.4 m²
= 32 m2^2 (nearest m²)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A large glamping tent is made up of four equal triangles and a square, as shown in the diagram below
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-I4-CA27-SA_5.svg 330 indent vpad
Bruce is covering the outside of the tent with waterproofing spray, not including the base. What is the area that Bruce will need to spray? Answer to the nearest square metre.
workedSolution
sm_nogap Area to spray
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 4.5 × 3.6| |= 32.4 m²| |= {{{correctAnswer0}}} {{{suffix0}}} (nearest m²)|
correctAnswer0
32
prefix0
suffix0
m$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer032

m2^2

Variant 3

DifficultyLevel

715

Question

A two person tent is made up of four equal triangles and a square, as shown in the diagram below



Jennifer is covering the outside of the tent with mosquito netting, not including the base.

What is the area that Jennifer will need to cover? Answer to the nearest square metre.

Worked Solution

Area to cover
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 2.6 × 2.1
= 10.92 m²
= 11 m2^2 (nearest m²)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A two person tent is made up of four equal triangles and a square, as shown in the diagram below
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-I4-CA27-SA_4.svg 330 indent vpad
Jennifer is covering the outside of the tent with mosquito netting, not including the base. What is the area that Jennifer will need to cover? Answer to the nearest square metre.
workedSolution
sm_nogap Area to cover
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 2.6 × 2.1| |= 10.92 m²| |= {{{correctAnswer0}}} {{{suffix0}}} (nearest m²)|
correctAnswer0
11
prefix0
suffix0
m$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer011

m2^2

Variant 4

DifficultyLevel

715

Question

A Christmas decoration is made up of four equal triangles and a square, as shown in the diagram below



Klaus is covering the outside of the decoration with glitter spray, not including the base.

What is the area that Klaus will need to cover? Answer to the nearest square centimetre.

Worked Solution

Area to cover
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 5.6 × 9.1
= 101.92 cm²
= 102 cm2^2 (nearest cm²)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A Christmas decoration is made up of four equal triangles and a square, as shown in the diagram below
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-I4-CA27-SA_3.svg 350 indent vpad
Klaus is covering the outside of the decoration with glitter spray, not including the base. What is the area that Klaus will need to cover? Answer to the nearest square centimetre.
workedSolution
sm_nogap Area to cover
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 5.6 × 9.1| |= 101.92 cm²| |= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm²)|
correctAnswer0
102
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0102

cm2^2

Variant 5

DifficultyLevel

714

Question

A small ancient pyramid has been excavated. The pyramid is made up of four equal triangles and a square, as shown in the diagram below



Della is calculating the outside surface area of the pyramid, not including the base.

What is the area that Della will calculate? Answer to the nearest square metre.

Worked Solution

Area to calculate
= 4 × 12bh\dfrac{1}{2}\large bh
= 4 × 12\dfrac{1}{2} × 15.2 × 12.7
= 386.08 m²
= 386 m2^2 (nearest m²)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A small ancient pyramid has been excavated. The pyramid is made up of four equal triangles and a square, as shown in the diagram below
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-I4-CA27-SA_2.svg 300 indent vpad
Della is calculating the outside surface area of the pyramid, not including the base. What is the area that Della will calculate? Answer to the nearest square metre.
workedSolution
sm_nogap Area to calculate
>>|| |-| |= 4 × $\dfrac{1}{2}\large bh$ | |= 4 × $\dfrac{1}{2}$ × 15.2 × 12.7| |= 386.08 m²| |= {{{correctAnswer0}}} {{{suffix0}}} (nearest m²)|
correctAnswer0
386
prefix0
suffix0
m$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0386

m2^2

Tags

  • ms_ca