Geometry, NAPX-H4-NC27

Question

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Worked Solution

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Variant 0

DifficultyLevel

700

Question

A regular hexagon has a perimeter of 30 cm.

Ima cuts it into 6 equilateral triangles.



What is the perimeter of one of the triangles?

Worked Solution

Length of one side of hexagon
= 30 ÷\div 5
= 5 cm

∴\therefore Perimeter = 5 + 5 + 5
= 15 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A regular hexagon has a perimeter of 30 cm. Ima cuts it into 6 equilateral triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/09/NAPX-H4-NC27.svg 260 indent2 vpad
What is the perimeter of one of the triangles?
workedSolution
sm_nogap Length of one side of hexagon
>||| |-|-| ||= 30 $\div$ 5| ||= 5 cm|

sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/09/NAPX-H4-NC27-Answer1.svg 110 indent3 vpad
||| |-|-| |$\therefore$ Perimeter|= 5 + 5 + 5| ||= {{{correctAnswer}}} |
correctAnswer
15 cm

Answers

Is Correct?Answer
x

5 cm

x

10 cm

x

12 cm

✓

15 cm

x

18 cm

Variant 1

DifficultyLevel

702

Question

A regular pentagon has a perimeter of 30 cm.

Ian cuts it into 5 isosceles triangles.



What is the perimeter of one of the isosceles triangles if the equal sides are 5 cm in length?

Worked Solution

Length of one side of hexagon
= 30 ÷\div 5
= 6 cm

∴\therefore Perimeter = 6 + 5 + 5
= 16 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A regular pentagon has a perimeter of 30 cm. Ian cuts it into 5 isosceles triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v1q.svg 260 indent2 vpad
What is the perimeter of one of the isosceles triangles if the equal sides are 5 cm in length?
workedSolution
sm_nogap Length of one side of hexagon
>||| |-|-| ||= 30 $\div$ 5| ||= 6 cm|

sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v1aws.svg 140 indent3 vpad
||| |-|-| |$\therefore$ Perimeter|= 6 + 5 + 5| ||= {{{correctAnswer}}} |
correctAnswer
16 cm

Answers

Is Correct?Answer
x

6 cm

x

10 cm

x

12 cm

x

15 cm

✓

16 cm

Variant 2

DifficultyLevel

704

Question

A regular octagon has a perimeter of 96 cm.

Uma cuts it into 8 isosceles triangles.



What is the perimeter of one of the isosceles triangles if the equal sides are 10 cm in length?

Worked Solution

Length of one side of hexagon
= 96 ÷\div 8
= 12 cm

∴\therefore Perimeter = 12 + 10 + 10
= 32 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A regular octagon has a perimeter of 96 cm. Uma cuts it into 8 isosceles triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v2aq.svg 340 indent2 vpad
What is the perimeter of one of the isosceles triangles if the equal sides are 10 cm in length?
workedSolution
sm_nogap Length of one side of hexagon
>||| |-|-| ||= 96 $\div$ 8| ||= 12 cm|

sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v2ws.svg 130 indent3 vpad
||| |-|-| |$\therefore$ Perimeter|= 12 + 10 + 10| ||= {{{correctAnswer}}} |
correctAnswer
32 cm

Answers

Is Correct?Answer
x

30 cm

✓

32 cm

x

36 cm

x

64 cm

x

80 cm

Variant 3

DifficultyLevel

701

Question

A regular dodecagon has a perimeter of 108 cm.

Iggy cuts it into 12 isosceles triangles.



What is the perimeter of one of the isosceles triangles if the equal sides are 15 cm in length?

Worked Solution

Length of one side of dodecagon
= 108 ÷\div 12
= 9 cm

∴\therefore Perimeter = 9 + 15 + 15
= 39 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A regular dodecagon has a perimeter of 108 cm. Iggy cuts it into 12 isosceles triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v4s.svg 340 indent2 vpad
What is the perimeter of one of the isosceles triangles if the equal sides are 15 cm in length?
workedSolution
sm_nogap Length of one side of dodecagon
>||| |-|-| ||= 108 $\div$ 12| ||= 9 cm|

sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v4ws.svg 120 indent3 vpad
||| |-|-| |$\therefore$ Perimeter|= 9 + 15 + 15| ||= {{{correctAnswer}}} |
correctAnswer
39 cm

Answers

Is Correct?Answer
x

9 cm

x

27 cm

✓

39 cm

x

45 cm

x

60 cm

Variant 4

DifficultyLevel

703

Question

A regular decagon has a perimeter of 240 cm.

Jorja cuts it into 10 isosceles triangles.



What is the perimeter of one of the isosceles triangles if the equal sides are 20 cm in length?

Worked Solution

Length of one side of decagon
= 240 ÷\div 10
= 24 cm

∴\therefore Perimeter = 24 + 20 + 20
= 64 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A regular decagon has a perimeter of 240 cm. Jorja cuts it into 10 isosceles triangles.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v3s.svg 320 indent2 vpad
What is the perimeter of one of the isosceles triangles if the equal sides are 20 cm in length?
workedSolution
sm_nogap Length of one side of decagon
>||| |-|-| ||= 240 $\div$ 10| ||= 24 cm|

sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-H4-NC27_v3sa.svg 130 indent3 vpad
||| |-|-| |$\therefore$ Perimeter|= 24 + 20 + 20| ||= {{{correctAnswer}}} |
correctAnswer
64 cm

Answers

Is Correct?Answer
x

24 cm

x

60 cm

✓

64 cm

x

72 cm

x

144 cm

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