Measurement, NAPX-F4-CA32 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

790

Question

An ancient civilisation created the following pattern in a large square field.



What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 80 ×\times 80
= 6400 m2^2

Area of next smallest square = 3200 m2^2

Area of next smallest square = 1600 m2^2
∴\therefore Shaded area = 34×\dfrac{3}{4}\times 1600
= 1200 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
An ancient civilisation created the following pattern in a large square field.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA32-SA.svg 300 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 80 $\times$ 80| |= 6400 m$^2$|

Area of next smallest square = 3200 m$^2$ Area of next smallest square = 1600 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{3}{4}\times$ 1600| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
1200
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
correctAnswer01200

m2^2

Variant 1

DifficultyLevel

793

Question

An ancient civilisation created the following pattern in a large square field.



What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 120 ×\times 120
= 14 400 m2^2

Area of next smallest square = 7200 m2^2

Area of next smallest square = 3600 m2^2
∴\therefore Shaded area = 14×\dfrac{1}{4}\times 7200 + 12×\dfrac{1}{2}\times 3600
= 1800 + 1800
= 3600 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
An ancient civilisation created the following pattern in a large square field.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/aebca96b-b270-4f44-80d6-e3a689067e0cv0_V3.svg 360 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 120 $\times$ 120| |= 14 400 m$^2$|

Area of next smallest square = 7200 m$^2$ Area of next smallest square = 3600 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{1}{4}\times$ 7200 + $\dfrac{1}{2}\times$ 3600| ||= 1800 + 1800| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
3600
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
correctAnswer03600

m2^2

Variant 2

DifficultyLevel

792

Question

An ancient civilisation created the following pattern in a large square field.



What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 80 ×\times 80
= 6400 m2^2

Area of next smallest square = 3200 m2^2

Area of next smallest square = 1600 m2^2
∴\therefore Shaded area = 12×\dfrac{1}{2}\times 3200 + 14×\dfrac{1}{4}\times 1600
= 1600 + 400
= 2000 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
An ancient civilisation created the following pattern in a large square field.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/aebca96b-b270-4f44-80d6-e3a689067e0cv0_V1.svg 400 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 80 $\times$ 80| |= 6400 m$^2$|

Area of next smallest square = 3200 m$^2$ Area of next smallest square = 1600 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{1}{2}\times$ 3200 + $\dfrac{1}{4}\times$ 1600| ||= 1600 + 400| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
2000
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
correctAnswer02000

m2^2

Variant 3

DifficultyLevel

794

Question

An ancient civilisation created the pattern below on a large mural.



What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 120 ×\times 120
= 14 400 m2^2

Area of next smallest square = 7200 m2^2

Area of next smallest square = 3600 m2^2
∴\therefore Shaded area = 12×\dfrac{1}{2}\times 14 400 + 34×\dfrac{3}{4}\times 3600
= 7200 + 2700
= 9900 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
An ancient civilisation created the pattern below on a large mural.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/aebca96b-b270-4f44-80d6-e3a689067e0cv0_V1-1.svg 400 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 120 $\times$ 120| |= 14 400 m$^2$|

Area of next smallest square = 7200 m$^2$ Area of next smallest square = 3600 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{1}{2}\times$ 14 400 + $\dfrac{3}{4}\times$ 3600| ||= 7200 + 2700| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
9900
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
correctAnswer09900

m2^2

Variant 4

DifficultyLevel

795

Question

A gardener was paving a large courtyard and created the following pattern.


What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 40 ×\times 40
= 1600 m2^2

Area of next smallest square = 800 m2^2

Area of next smallest square = 400 m2^2
∴\therefore Shaded area = 14×\dfrac{1}{4}\times 1600 + 12×\dfrac{1}{2}\times 800 + + 14×\dfrac{1}{4}\times 400
= 400 + 400 + 100
= 900 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
A gardener was paving a large courtyard and created the following pattern.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/aebca96b-b270-4f44-80d6-e3a689067e0cv0_V5.svg 400 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 40 $\times$ 40| |= 1600 m$^2$|

Area of next smallest square = 800 m$^2$ Area of next smallest square = 400 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{1}{4}\times$ 1600 + $\dfrac{1}{2}\times$ 800 + + $\dfrac{1}{4}\times$ 400| ||= 400 + 400 + 100| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
900
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
correctAnswer0900

m2^2

Variant 5

DifficultyLevel

789

Question

A gardener was paving a large courtyard and created the following pattern.



What is the size of the shaded area in the pattern?

Worked Solution

Total area of the largest square
= 120 ×\times 120
= 14 400 m2^2

Area of next smallest square = 7200 m2^2

Area of next smallest square = 3600 m2^2
∴\therefore Shaded area = 12×\dfrac{1}{2}\times 14 400 + 34×\dfrac{3}{4}\times 3600
= 7200 + 2700
= 9900 m2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
A gardener was paving a large courtyard and created the following pattern.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/aebca96b-b270-4f44-80d6-e3a689067e0cv0_V1-1.svg 400 indent3 vpad
What is the size of the shaded area in the pattern?
workedSolution
sm_nogap Total area of the largest square
>>|| |-| |= 120 $\times$ 120| |= 14 400 m$^2$|

Area of next smallest square = 7200 m$^2$ Area of next smallest square = 3600 m$^2$
||| |-|-| |$\therefore$ Shaded area|= $\dfrac{1}{2}\times$ 14 400 + $\dfrac{3}{4}\times$ 3600| ||= 7200 + 2700| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
9900
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
correctAnswer09900

m2^2

Tags

  • ms_ca