Measurement, NAPX-F4-CA08

Question

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Worked Solution

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Variant 0

DifficultyLevel

562

Question

A trapezium is constructed on a grid of 10 rectangles.

Each rectangle measures 3 cm × 7 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1
Area 1 rectangle = 3 × 7
= 21 cm2^2

∴\therefore Total Area = (6 × 21) + 2 triangles
= 126 + 2 × (12×3×14)\bigg( \dfrac{1}{2} \times 3 \times 14 \bigg)
= 126 + 42
= 168 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×14×(9+15)\dfrac{1}{2} \times 14 \times (9+15)
= 7×247 \times 24
= 168 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 10 rectangles. Each rectangle measures 3 cm × 7 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA08.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1 ||| |-|-| |Area 1 rectangle|= 3 × 7| ||= 21 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (6 × 21) + 2 triangles| ||= 126 + 2 × $\bigg( \dfrac{1}{2} \times 3 \times 14 \bigg)$| ||= 126 + 42| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 14 \times (9+15)$| ||= $7 \times 24$| ||= {{{correctAnswer}}}|
correctAnswer
168 cm$^2$

Answers

Is Correct?Answer
x

150 cm2^2

✓

168 cm2^2

x

189 cm2^2

x

210 cm2^2

Variant 1

DifficultyLevel

563

Question

A trapezium is constructed on a grid of 28 rectangles.

Each rectangle measures 2 cm × 6 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1
Area 1 rectangle = 2 × 6
= 12 cm2^2

∴\therefore Total Area = (12 × 12) + 2 triangles
= 144 + 2 × (12×4×24)\bigg( \dfrac{1}{2} \times 4 \times 24 \bigg)
= 144 + 96
= 240 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×24×(14+6)\dfrac{1}{2} \times 24 \times (14+6)
= 12×2012 \times 20
= 240 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 28 rectangles. Each rectangle measures 2 cm × 6 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v1.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1 ||| |-|-| |Area 1 rectangle|= 2 × 6| ||= 12 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (12 × 12) + 2 triangles| ||= 144 + 2 × $\bigg( \dfrac{1}{2} \times 4 \times 24 \bigg)$| ||= 144 + 96| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 24 \times (14+6)$| ||= $12 \times 20$| ||= {{{correctAnswer}}}|
correctAnswer
240 cm$^2$

Answers

Is Correct?Answer
x

144 cm2^2

✓

240 cm2^2

x

288 cm2^2

x

336 cm2^2

Variant 2

DifficultyLevel

561

Question

A trapezium is constructed on a grid of 16 rectangles.

Each rectangle measures 3 cm × 5 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1
Area 1 rectangle = 5 × 3
= 15 cm2^2

∴\therefore Total Area = (8 × 15) + 2 triangles
= 120 + 2 × (12×5×12)\bigg( \dfrac{1}{2} \times 5 \times 12 \bigg)
= 120 + 60
= 180 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×12×(20+10)\dfrac{1}{2} \times 12 \times (20+10)
= 6×306 \times 30
= 180 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 16 rectangles. Each rectangle measures 3 cm × 5 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v3.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1 ||| |-|-| |Area 1 rectangle|= 5 × 3| ||= 15 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (8 × 15) + 2 triangles| ||= 120 + 2 × $\bigg( \dfrac{1}{2} \times 5 \times 12 \bigg)$| ||= 120 + 60| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 12 \times (20+10)$| ||= $6 \times 30$| ||= {{{correctAnswer}}}|
correctAnswer
180 cm$^2$

Answers

Is Correct?Answer
x

120 cm2^2

x

150 cm2^2

✓

180 cm2^2

x

240 cm2^2

Variant 3

DifficultyLevel

560

Question

A trapezium is constructed on a grid of 24 rectangles.

Each rectangle measures 4 cm × 7 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1
Area 1 rectangle = 4 × 7
= 28 cm2^2

∴\therefore Total Area = (18 × 28) + 2 triangles
= 504 + 2 × (12×4×21)\bigg( \dfrac{1}{2} \times 4 \times 21 \bigg)
= 504 + 84
= 588 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×21×(32+24)\dfrac{1}{2} \times 21 \times (32+24)
= 10.5×5610.5 \times 56
= 588 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 24 rectangles. Each rectangle measures 4 cm × 7 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v2.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1 ||| |-|-| |Area 1 rectangle|= 4 × 7| ||= 28 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (18 × 28) + 2 triangles| ||= 504 + 2 × $\bigg( \dfrac{1}{2} \times 4 \times 21 \bigg)$| ||= 504 + 84| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 21 \times (32+24)$| ||= $10.5 \times 56$| ||= {{{correctAnswer}}}|
correctAnswer
588 cm$^2$

Answers

Is Correct?Answer
x

294 cm2^2

x

336 cm2^2

✓

588 cm2^2

x

672 cm2^2

Variant 4

DifficultyLevel

564

Question

A trapezium is constructed on a grid of 21 rectangles.

Each rectangle measures 4 cm × 10 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1
Area 1 rectangle = 4 × 10
= 40 cm2^2

∴\therefore Total Area = (9 × 40) + triangle 1 + triangle 2
= 9 × 40 + (12×4×30)\bigg( \dfrac{1}{2} \times 4 \times 30 \bigg) + (12×12×30)\bigg( \dfrac{1}{2} \times 12 \times 30 \bigg)
= 360 + 60 + 180
= 600 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×30×(28+12)\dfrac{1}{2} \times 30 \times (28+12)
= 15×4015 \times 40
= 600 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 21 rectangles. Each rectangle measures 4 cm × 10 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v4.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v4_ws.svg 260 indent3 vpad ||| |-|-| |Area 1 rectangle|= 4 × 10| ||= 40 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (9 × 40) + triangle 1 + triangle 2| ||= 9 × 40 + $\bigg( \dfrac{1}{2} \times 4 \times 30 \bigg)$ + $\bigg( \dfrac{1}{2} \times 12 \times 30 \bigg)$| ||= 360 + 60 + 180| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 30 \times (28+12)$| ||= $15 \times 40$| ||= {{{correctAnswer}}}|
correctAnswer
600 cm$^2$

Answers

Is Correct?Answer
x

240 cm2^2

x

360 cm2^2

x

420 cm2^2

✓

600 cm2^2

Variant 5

DifficultyLevel

564

Question

A trapezium is constructed on a grid of 28 rectangles.

Each rectangle measures 3 cm × 5 cm.



What is the area of the trapezium?

Worked Solution

Strategy 1

Area 1 rectangle = 3 × 5
= 15 cm2^2

∴\therefore Total Area = (8 × 15) + triangle 1 + triangle 2
= 8 × 15 + (12×9×20)\bigg( \dfrac{1}{2} \times 9 \times 20 \bigg) + (12×6×20)\bigg( \dfrac{1}{2} \times 6 \times 20 \bigg)
= 120 + 90 + 60
= 270 cm2^2

Strategy 2 (advanced)
Area of trapezium = 12×\dfrac{1}{2} \times height × (a\times\ (\large a + b\large b)
= 12×20×(21+6)\dfrac{1}{2} \times 20 \times (21+6)
= 10×2710 \times 27
= 270 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A trapezium is constructed on a grid of 28 rectangles. Each rectangle measures 3 cm × 5 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v5.svg 240 indent3 vpad
What is the area of the trapezium?
workedSolution
Strategy 1
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA08_v5_ws.svg 260 indent3 vpad ||| |-|-| |Area 1 rectangle|= 3 × 5| ||= 15 cm$^2$|

||| |-|-| |$\therefore$ Total Area|= (8 × 15) + triangle 1 + triangle 2| ||= 8 × 15 + $\bigg( \dfrac{1}{2} \times 9 \times 20 \bigg)$ + $\bigg( \dfrac{1}{2} \times 6 \times 20 \bigg)$| ||= 120 + 90 + 60| ||= {{{correctAnswer}}}|

Strategy 2 (advanced)
||| |-|-| |Area of trapezium|= $\dfrac{1}{2} \times$ height $\times\ (\large a$ + $\large b$)| ||= $\dfrac{1}{2} \times 20 \times (21+6)$| ||= $10 \times 27$| ||= {{{correctAnswer}}}|
correctAnswer
270 cm$^2$

Answers

Is Correct?Answer
x

18 cm2^2

x

135 cm2^2

x

210 cm2^2

✓

270 cm2^2

Tags

  • ms_ca