Measurement, NAPX-E4-NC29 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

668

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 112 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 7 squares

Area of 1 square

= 112 ÷ 7

= 16 cm2^2

∴\therefore Side length of each square

= 16\sqrt{16}

= 4 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2017/01/NAP-E4-NC29-150x150.png 160 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 112 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 7 squares sm_nogap Area of 1 square >> = 112 ÷ 7 >> = 16 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{16}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
4
prefix0
suffix0
cm

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
correctAnswer04

cm

Variant 1

DifficultyLevel

667

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 360 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 10 squares

Area of 1 square

= 360 ÷ 10

= 36 cm2^2

∴\therefore Side length of each square

= 36\sqrt{36}

= 6 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-NC29-SA_v1.svg 180 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 360 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 10 squares sm_nogap Area of 1 square >> = 360 ÷ 10 >> = 36 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{36}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
6
prefix0
suffix0
cm

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
correctAnswer06

cm

Variant 2

DifficultyLevel

671

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 686 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 14 squares

Area of 1 square

= 686 ÷ 14

= 49 cm2^2

∴\therefore Side length of each square

= 49\sqrt{49}

= 7 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-NC29-SA_v2.svg 180 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 686 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 14 squares sm_nogap Area of 1 square >> = 686 ÷ 14 >> = 49 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{49}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
7
prefix0
suffix0
cm

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
correctAnswer07

cm

Variant 3

DifficultyLevel

670

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 450 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 18 squares

Area of 1 square

= 450 ÷ 18

= 25 cm2^2

∴\therefore Side length of each square

= 25\sqrt{25}

= 5 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-NC29-SA_v3.svg 270 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 450 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 18 squares sm_nogap Area of 1 square >> = 450 ÷ 18 >> = 25 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{25}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
5
prefix0
suffix0
cm

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
correctAnswer05

cm

Variant 4

DifficultyLevel

674

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 1782 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 22 squares

Area of 1 square

= 1782 ÷ 22

= 81 cm2^2

∴\therefore Side length of each square

= 81\sqrt{81}

= 9 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-NC29-SA_v4.svg 300 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 1782 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 22 squares sm_nogap Area of 1 square >> = 1782 ÷ 22 >> = 81 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{81}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
9
prefix0
suffix0
cm

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
correctAnswer09

cm

Variant 5

DifficultyLevel

675

Question

The octagon below is divided into identical squares and identical triangles.



The area of the octagon is a multiple of the area of one of the squares.

The area of the octagon is 1792 cm2^2.

What is the side length of each square?

Worked Solution

Area of octagon in squares

= 28 squares

Area of 1 square

= 1792 ÷ 28

= 64 cm2^2

∴\therefore Side length of each square

= 64\sqrt{64}

= 8 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The octagon below is divided into identical squares and identical triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-E4-NC29-SA_v5.svg 300 indent3 vpad
The area of the octagon is a multiple of the area of one of the squares. The area of the octagon is 1792 cm$^2$. What is the side length of each square?
workedSolution
sm_nogap Area of octagon in squares >> = 28 squares sm_nogap Area of 1 square >> = 1792 ÷ 28 >> = 64 cm$^2$ sm_nogap $\therefore$ Side length of each square >>= $\sqrt{64}$ >>= {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
8
prefix0
suffix0
cm

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
correctAnswer08

cm

Tags

  • ms_ca