Measurement, NAPX-F4-NC24 SA, NAPX-F3-NC27 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

695

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×12×12\dfrac{1}{2} \times 12 \times 12
= 72 cm2^2

Area of smaller triangle
= 12×4×4\dfrac{1}{2} \times 4 \times 4
= 8 cm2^2

∴\therefore Shaded area
= 72 − (2 × 8)
= 56 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-NC24.svg 350 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 12 \times 12$| |= 72 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 4 \times 4$| |= 8 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 72 − (2 × 8)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
56
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
correctAnswer056

cm2^2

Variant 1

DifficultyLevel

698

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×16×16\dfrac{1}{2} \times 16 \times 16
= 128 cm2^2

Area of smaller triangle
= 12×6×6\dfrac{1}{2} \times 6 \times 6
= 18 cm2^2

∴\therefore Shaded area
= 128 − (2 × 18)
= 92 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-NC24-SA_NAPX-F3-NC27-SA_v1.svg 400 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 16 \times 16$| |= 128 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 6 \times 6$| |= 18 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 128 − (2 × 18)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
92
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
correctAnswer092

cm2^2

Variant 2

DifficultyLevel

691

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×10×10\dfrac{1}{2} \times 10 \times 10
= 50 cm2^2

Area of smaller triangle
= 12×3×3\dfrac{1}{2} \times 3 \times 3
= 4.5 cm2^2

∴\therefore Shaded area
= 50 − (2 × 4.5)
= 41 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-NC24-SA_NAPX-F3-NC27-SA_v2.svg 400 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 10 \times 10$| |= 50 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 3 \times 3$| |= 4.5 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 50 − (2 × 4.5)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
41
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
correctAnswer041

cm2^2

Variant 3

DifficultyLevel

695

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×20×20\dfrac{1}{2} \times 20 \times 20
= 200 cm2^2

Area of smaller triangle
= 12×8×8\dfrac{1}{2} \times 8 \times 8
= 32 cm2^2

∴\therefore Shaded area
= 200 − (2 × 32)
= 136 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-NC24-SA_NAPX-F3-NC27-SA_v3.svg 400 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 20 \times 20$| |= 200 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 8 \times 8$| |= 32 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 200 − (2 × 32)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
136
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
correctAnswer0136

cm2^2

Variant 4

DifficultyLevel

694

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×20×20\dfrac{1}{2} \times 20 \times 20
= 200 cm2^2

Area of smaller triangle
= 12×5×5\dfrac{1}{2} \times 5 \times 5
= 12.5 cm2^2

∴\therefore Shaded area
= 200 − (2 × 12.5)
= 175 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-NC24-SA_NAPX-F3-NC27-SA_v4.svg 400 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 20 \times 20$| |= 200 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 5 \times 5$| |= 12.5 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 200 − (2 × 12.5)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
175
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
correctAnswer0175

cm2^2

Variant 5

DifficultyLevel

713

Question


What is the area of the shaded part of the figure?

Worked Solution

Area of large triangle
= 12×12×12\dfrac{1}{2} \times 12 \times 12
= 72 cm2^2

Area of smaller triangle
= 12×3.6×3.6\dfrac{1}{2} \times 3.6 \times 3.6
= 6.48 cm2^2

∴\therefore Shaded area
= 72 − (2 × 6.48)
= 59.04 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-NC24-SA_NAPX-F3-NC27-SA_v5.svg 400 indent3 vpad
What is the area of the shaded part of the figure?
workedSolution
sm_nogap Area of large triangle
>>|| |-| |= $\dfrac{1}{2} \times 12 \times 12$| |= 72 cm$^2$|

sm_nogap Area of smaller triangle
>>|| |-| |= $\dfrac{1}{2} \times 3.6 \times 3.6$| |= 6.48 cm$^2$|

sm_nogap $\therefore$ Shaded area
>>|| |-| |= 72 − (2 × 6.48)| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
59.04
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
correctAnswer059.04

cm2^2

Tags

  • ms_ca