SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Unit Conversion, SM-Bank 023

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = ________ m  ×  ________ m = ______________ km²   (1 mark)

  1. The Barangaroo precinct in Sydney has a total floor space of 681 000 square metres.
  2. Find the area of this floor space in square kilometres.  (1 mark)
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a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)

b.    \(0.681\ \text{km}^{2}\)

Show Worked Solution

a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)
 

b.    \(\text{Area}\) \(= \dfrac{681\ 000}{1\ 000\ 000}\)  
  \(=0.681\ \text{km}^{2}\)  

Unit Conversion, SM-Bank 022

  1. By considering the dimensions of a square with an area of 1 square kilometre, complete the unit conversion equation below:

1 km² = _______ m  ×  _______ m = ____________ km²   (1 mark)

  1. A rural property is in the shape of a rectangle with sides of length 1.20 kilometres and 2.36 kilometres.
  2. Find the area of the property in square kilometres and using the conversion equation, express the area in square metres.  (2 marks)
Show Answers Only

a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)

b.    \(2\ 832\ 000\ \text{m}^{2}\)

Show Worked Solution

a.    \(1\ \text{km}^{2} = 1000\ \text{m}\ \times\ 1000\ \text{m}\ = 1\ 000\ 000\ \text{km}^{2} \)
 

b.    \(\text{Area}\) \(= 1.20 \times 2.36\)  
  \(=2.832\ \text{km}^{2}\)  
  \(=2.832 \times 1\ 000\ 000\  \text{m}^{2}\)  
  \(=2\ 832\ 000\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 021

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular poster has an area of 0.09\(\pi\) square metres.
  2. Express this area in square centimetres, giving your answer in exact form.  (1 mark)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(900\pi\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{0.09}\pi\ \text{m}^{2}\) \(= 0.09\pi \times 10\ 000 \)  
  \(=900\pi\ \text{cm}^2 \)

Unit Conversion, SM-Bank 020

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular stage has an area of 265 000 square centimetres.
  2. Express this area in square metres.  (1 mark)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(26\ \text{m}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{265 000 cm}^{2}\) \(= \dfrac{26\ 000}{10\ 000}\)  
  \(=26\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 019

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A rectangular serviette has an area of 0.075 square metres.
  2. Express this area in square centimetres.  (1 mark)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(750\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{0.075 m}^{2}\) \(=0.075 \times 10\ 000\)  
  \(=750\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 018

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A doubles tennis court has an area of 260 square metres.
  2. Express this area in square centimetres.  (1 mark)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(2\ 600\ 000\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{260 m}^{2}\) \(=260 \times 10\ 000\)  
  \(=2\ 600\ 000\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 017

  1. By considering the dimensions of a square with an area of 1 square metre, complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = __________ cm²   (1 mark)

  1. A circular elevator has a diameter of 1.6 metres.
  2. Find the area of the elevator's floor in square metres and using the conversion equation, express the area to the nearest square centimetre.  (2 marks)
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a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(20\ 106\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(\text{Radius}\ =\dfrac{1.6}{2} = 0.8\ \text{m} \)

\(\text{Area}\) \(=\pi \times 0.8^2\)  
  \(=2.01061…\ \text{m}^{2}\)  
  \(=2.01061… \times 10\ 000\ \text{cm}^{2}\)  
  \(=20\ 106\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 016

The square below has an area of 1 square metre.
 

  1. Complete the unit conversion equation below:

1 m² = _____ cm  ×  _____ cm = _______ cm²   (1 mark)

  1. A circular playground has an area of 2000 square metres.
  2. Using the conversion equation, or otherwise, express the area in square centimetres.  (1 mark)
Show Answers Only

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

b.    \(20\ 000\ 000\ \text{mm}^{2}\)

Show Worked Solution

a.    \(1\ \text{m}^{2} = 100\ \text{cm}\ \times\ 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)
 

b.    \(2000\ \text{m}^{2}\) \(= 2000 \times 10\ 000\ \text{cm}^{2} \)
  \(= 20\ 000\ 000\ \text{cm}^{2} \)

Unit Conversion, SM-Bank 015

The square below has an area of 1 square centimetre.
 

  1. Complete the unit conversion equation below:

1 cm² = _____ mm  ×  _____ mm = _______ mm²   (1 mark)

  1. A rectangle has an area of 1100 square millimetres.
  2. Using the conversion equation, or otherwise, express the area of the circle in square centimetres.  (1 mark)
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a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)

b.    \(11\ \text{cm}^{2}\)

Show Worked Solution

a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)
 

b.    \(1100\ \text{mm}^{2}\) \(= \dfrac{1100}{100} \)
  \(=11\ \text{cm}^{2} \)

Unit Conversion, SM-Bank 014

  1. By considering the dimensions of a square with an area of 1 square centimetre, complete the unit conversion equation below:

1 cm² = _____ mm  ×  _____ mm = _______ mm²   (1 mark)

  1. A circle has an area of 950 square centimetres.
  2. Using the conversion equation, or otherwise, express the area of the circle in square millimetres.  (1 mark)
Show Answers Only

a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)

b.    \(95\ 000\ \text{mm}^{2}\)

Show Worked Solution

a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)
 

b.    \(900\ \text{cm}^{2}\) \(= 900 \times 100\ \text{mm}^{2} \)
  \(= 90\ 000\ \text{mm}^{2} \)

Unit Conversion, SM-Bank 013

The square below has an area of 1 square centimetre.
 

  1. Complete the unit conversion equation below:

1 cm² = _____ mm  ×  _____ mm = _______ mm²   (1 mark)

  1. A square has an area of 125 square centimetres.
  2. Using the conversion equation, or otherwise, express the area of the rectangle in square millimetres.  (1 mark)
Show Answers Only

a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)

b.    \(12\ 500\ \text{mm}^{2}\)

Show Worked Solution

a.    \(1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} \)
 

b.    \(125\ \text{cm}^{2}\) \(= 125 \times 100\ \text{mm}^{2} \)
  \(= 12\ 500\ \text{mm}^{2} \)

Unit Conversion, SM-Bank 012

The Google main campus in California covers an area of 137 500 square metres.

Using the conversion ratio, 1 hectare = 10 000 m², determine the area of the property in hectares.  (1 mark)

Show Answers Only

\( 13.75\ \text{ha}\)

Show Worked Solution
\(\text{Area}\) \(= \dfrac{137\ 500}{10\ 000}\ \text{ha} \)  
  \(= 13.75\ \text{ha}\)  

Unit Conversion, SM-Bank 011

A property in Coonamble is in the shape of a rectangle with sides 1400 metres and 2200 metres in length.

Using the conversion ratio, 1 hectare = 10 000 m², determine the area of the property in hectares.  (2 marks)

Show Answers Only

\( 308\ \text{ha}\)

Show Worked Solution
\(\text{Area}\) \(= 1400 \times 2200\ \text{m}^{2} \)  
  \(= 3\ 080\ 000\ \text{m}^{2}\)  
  \(= \dfrac{3\ 080\ 000}{10\ 000} \)  
  \(=308\ \text{ha} \)  

Unit Conversion, SM-Bank 010

A circle is drawn from a city centre with a radius of 800 metres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the area of the circle in square kilometres, to two decimal places.  (2 marks)

Show Answers Only

\( 2.01 \text{km}^{2}\)

Show Worked Solution
\(\text{Area}\) \(= \pi \times 800^{2}\ \text{m}^{2} \)  
  \(= 2\ 010\ 619\ \text{m}^{2}\)  
  \(= \dfrac{2\ 010\ 619}{1\ 000\ 000} \)  
  \(=2.01\ \text{km}^{2} \)  

Unit Conversion, SM-Bank 009

A Queensland outback pastoralist owns a property with an area of 500 square kilometres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the exact area of the property in square metres.  (2 marks)

Show Answers Only

\( 500\ 000\ 000\ \text{m}^{2}\)

Show Worked Solution
\(\text{Area}\) \(= 500 \times 1\ 000\ 000\)  
  \(= 500\ 000\ 000\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 008

A circle has a radius of 60 centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the exact area of the circle in square metres.  (2 marks)

Show Answers Only

\(\ 0.36\pi\ \text{m}^{2}\)

Show Worked Solution
\(\text{Area}\) \(= \pi \times 60^{2}\)  
  \(=3600\pi\ \text{cm}^{2}\)  
  \(= \dfrac{3600}{10\ 000}\pi\ \text{m}^{2}\)  
  \(= 0.36\pi\ \text{m}^2 \)  

Unit Conversion, SM-Bank 007

A poster has an area of 2500 square centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres.  (1 mark)

Show Answers Only

\(0.25\ \text{m}^{2}\)

Show Worked Solution
\(2500\ \text{cm}^{2}\) \(= \dfrac{2500}{10\ 000}\ \text{m}^2\)  
  \(=0.25\ \text{m}^{2}\)  

Unit Conversion, SM-Bank 006

Athletes throw shot puts from a shot put circle with a standard diameter of 2.13 metres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the area of a shot put circle to the nearest square centimetres.  (3 marks)

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\(8\ \text{cm}^{2}\)

Show Worked Solution

\(\text{Radius}\ = \dfrac{2.13}{2} = 1.065\ \text{m}\)

\(\text{Area}\) \(= \pi \times 1.065^{2}\)  
  \(=3.56327… \text{m}^{2}\)  
  \(=3.56327… \times 10\ 000\ \text{cm}^{2}\)  
  \(=35\ 633\ \text{cm}^2\ \ (\text{nearest cm}^2) \)  

Unit Conversion, SM-Bank 005

A pickleball court has an area of 81.74 square metres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres.  (1 mark)

Show Answers Only

\(817\ 400\ \text{cm}^{2}\)

Show Worked Solution
\(81.74\ \text{m}^{2}\) \(= 81.74 \times 10\ 000\ \text{cm}^2\)  
  \(=817\ 400\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 004

The end of a cylinder has an area of 60 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres.  (1 mark)

Show Answers Only

\(0.6\ \text{cm}^{2}\)

Show Worked Solution
\(60\ \text{mm}^{2}\) \(= \dfrac{60}{100}\ \text{cm}^2\)  
  \(=0.6\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 003

One side of an Australian 10-cent coin has an area of 437 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres.  (1 mark)

Show Answers Only

\(4.37\ \text{cm}^{2}\)

Show Worked Solution
\(437\ \text{mm}^{2}\) \(= \dfrac{437}{100}\ \text{cm}^2\)  
  \(=4.37\ \text{cm}^{2}\)  

Unit Conversion, SM-Bank 002

A circle with radius 1 cm, has an area of \(\pi\) square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the circle in square millimetres.  (1 mark)

Show Answers Only

\(100\pi\ \text{mm}^{2}\)

Show Worked Solution
\(\pi\ \text{cm}^{2}\) \(= \pi \times 100\ \text{mm}^2\)  
  \(=100\pi\ \text{mm}^{2}\)  

Unit Conversion, SM-Bank 001

A rectangle has an area of 450 square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the rectangle in square millimetres.  (1 mark)

Show Answers Only

\(45\ 000\ \text{mm}^{2}\)

Show Worked Solution
\(450\ \text{cm}^{2}\) \(= 450 \times 100\ \text{mm}^{2} \)
  \(= 45\ 000\ \text{mm}^{2} \)

Area, SM-Bank 094

A poster has an area of 5250 square centimetres.

Find the area of the poster in square millimetres?   (2 marks)

Show Answers Only

\(525\ 000\ \text{mm}^{2}\)

Show Worked Solution

\(\text{1 cm}^{2}\ = 10\ \text{mm}\ \times 10\ \text{mm} = 100\ \text{mm}^{2} \)

\(\text{5250 cm}^{2} = 5250 \times 100 = 525\ 000\ \text{mm}^{2}\)

Area, SM-Bank 091

A walled city has a land area of 950 hectares.

Express the area of the city in square kilometres.  (2 marks)

Show Answers Only

\(9.5\ \text{km}^2\)

Show Worked Solution

\(\text{1 hectare}\ = 10\ 000\ \text{m}^{2}\)

\(\text{950 hectares}\ = 950 \times 10\ 000 = 9\ 500\ 000\ \text{m}^{2} \)

\(\text{1 km}^{2}\ = 1000\ \text{m} \times 1000\ \text{m}\ = 1\ 000\ 000\ \text{m}^{2}\)

\(\text{950 hectares}\ = \dfrac{9\ 500\ 000}{1\ 000\ 000} = 9.5\ \text{km}^{2} \)

Area, SM-Bank 090

Jim has a hobby farm with an area of 7 hectares.

What is the size of Jim's farm in square metres.   (1 mark)

Show Answers Only

\(70\ 000\ \text{m}^2\)

Show Worked Solution

\(\text{1 hectare}\ = 10\ 000\ \text{m}^{2} \)

\(\text{7 hectares}\ = 7 \times 10\ 000 = 70\ 000\ \text{m}^{2} \)

Area, SM-Bank 089

Express an area of 0.003 square metres in square millimetres.  (2 marks)

Show Answers Only

\(3000\ \text{mm}^2\)

Show Worked Solution

\(\text{1 m}^{2}\ =1000\ \text{mm}\times 1000\ \text{mm} =1\ 000\ 000\ \text{mm}^2\)

\(\text{0.003 m}^{2}\ = 0.003 \times 1\ 000\ 000 = 3000\ \text{mm}^{2} \)

Area, SM-Bank 088

Convert an area of 9 300 000 square metres into square kilometres.  (1 mark)

Show Answers Only

\(9.3\ \text{km}^2\)

Show Worked Solution

\(\text{1 km}^{2} =1000\ \text{m}\times 1000\ \text{m}\ =1\ 000\ 000\ \text{m}^2\)

\(\text{9 300 000 m}^{2} =\dfrac{9\ 300\ 000}{1\ 000\ 000}=9.3\ \text{km}^2\)

Area, SM-Bank 087

A dining table has an area of 35 700 square centimetres.

Express this area in square metres.  (1 mark)

Show Answers Only

\(3.57\ \text{m}^2\)

Show Worked Solution

\(\text{1 m}^{2}\ = 100\ \text{cm}\times 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2} \)

\(\text{35 700 cm}^{2} = \dfrac{35\ 700}{10\ 000} = 3.57\ \text{m}^2\)

Area, SM-Bank 086

Convert an area of 500 square millimetres to square centimetres.  (1 mark)

Show Answers Only

\(5\ \text{cm}^2\)

Show Worked Solution

\(\text{1 cm}^{2}\ =10\ \text{mm}\times 10\ \text{mm}\ =100\ \text{mm}^2\)

\(500\ \text{mm}^2 =\dfrac{500}{100} =5\ \text{cm}^2\)

Area, SM-Bank 085

A remote island has a land area of 4.6 square kilometres.

Convert this area into square metres.  (1 mark)

Show Answers Only

\(4\ 600\ 000\ \text{m}^2\)

Show Worked Solution

\( \text{1 km}^{2}\ =1000\ \text{m} \times 1000\ \text{m} = 1\ 000\ 000\ \text{m}^2 \)

\(\text{4.6 km}^{2}\ = 4.6\times 1\ 000\ 000=4\ 600\ 000\ \text{m}^2 \)

Area, SM-Bank 084

Convert an area of 15 square metres to square centimetres.  (1 mark)

Show Answers Only

\(150\ 000\ \text{cm}^2\)

Show Worked Solution

\(\text{1 m}^{2} = 100\ \text{cm}\times 100\ \text{cm}=10\ 000\ \text{cm}^2\)

\(\text{15 m}^{2}\ = 15 \times 10\ 000 = 150\ 000\ \text{cm}^2\)

Area, SM-Bank 083

Convert an area of 3 square centimetres to square millimetres.   (1 mark)

Show Answers Only

\(300\ \text{mm}^2\)

Show Worked Solution

\(\text{1 cm}^{2} = 10\ \text{mm}\times 10\ \text{mm}\ =100\ \text{mm}^2\)

\(\text{3 cm}^{2} = 3 \times 100 = 300\ \text{mm}^2\)

 

Area, SM-Bank 082

Julia bought a kitchen rug with an area of 0.85 square metres.

What is the area of the kitchen rug in square centimetres?   (2 marks)

Show Answers Only

\(8500\ \text{cm}^{2} \) 

Show Worked Solution

\(\text{1 m}^{2} = 100\ \text{cm} \times 100\ \text{cm}\ =10\ 000\ \text{cm}^{2} \)

\(\text{0.85 m}^{2} = 0.85 \times 10\ 000 = 8500\ \text{cm}^{2} \) 

Area, SM-Bank 081 MC

Ben bought a dog mat with an area of 0.5 square metres.

What is the area of the dog mat in square centimetres?

  1. \(2.5\ \text{cm}^2\)
  2. \(5\ \text{cm}^2\)
  3. \(5000\ \text{cm}^2\)
  4. \(25\ 000\ \text{cm}^2\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{1 m}^{2} =100\ \text{cm}\times 100\ \text{cm} = 10\ 000\ \text{cm}^{2} \)

\(\text{0.5 m}^{2} = 0.5\times 10\ 000 =5000\ \text{cm}^2\)  

\(\Rightarrow C\)

Area, SM-Bank 077

Vlad has a giant chess board that has an area of 4 square metres.

What is the area of the chess board in square centimetres?  (2 marks)

Show Answers Only

\(40\ 000\ \text{square centimetres}\)

Show Worked Solution

\(\text{Strategy 1 (convert square metres):}\)

\(\text{1 m}^{2} = 100\ \text{cm}\ \times 100\ \text{cm}\ = 10\ 000\ \text{cm}^{2}\)

\(\text{Side length}\ =\sqrt{4} =2\ \text{m}\)

\(\text{Area}\ =2^2 = 4\ \text{m}\ = 4 \times 10\ 000 = 40\ 000\ \text{cm}^{2}\)
 

\(\text{Strategy 2 (convert sides to centimetres):}\)

\(\text{Side length}\ =\sqrt{4} =2\ \text{m}\ = 200\ \text{cm}\)

\(\text{Area}\ =200^2 = 40\ 000\ \text{square centimetres}\)

Area, SM-Bank 076

Jeremy's back deck is square in shape and has an area of 16 square metres.

What is the area of the deck in square centimetres?  (2 marks)

Show Answers Only

\(160\ 000\ \text{square centimetres}\)

Show Worked Solution

\(\text{Strategy 1 (convert square metres):}\)

\(\text{1 m}^{2} = 100\ \text{cm}\ \times 100\ \text{cm}\ = 10\ 000\ \text{cm}^2 \)

\(\text{Side length of deck}\ =\sqrt{16} =4\ \text{m}\)

\(\text{Area} =4^2 = 16\ \text{m}^{2} = 16 \times 10\ 000 = 160\ 000\ \text{cm}^{2}\)
 

\(\text{Strategy 2 (convert side lengths):}\)

\(\text{Side length of deck}\ =\sqrt{16} =4\ \text{m}= 4 \times 100 = 400\ \text{cm}\)

\(\text{Area} =400^2 =160\ 000\ \text{cm}^{2}\)

Area, SM-Bank 075

A square fridge magnet has an area of 900 square millimetres.

What is the area of the fridge magnet in square centimetres?  (2 marks)

Show Answers Only

\(9\ \text{cm}^2\)

Show Worked Solution

\(\text{Strategy 1 (convert square millimetres):}\)

\(\text{1 cm}^{2}\ = 10\ \text{mm}\ \times 10\ \text{mm}\ = 100\ \text{mm}^{2} \)

\(\text{Side length}\ =\sqrt{900}\ = 30\ \text{mm}\)

\(\text{Area} =30^2 =900\ \text{mm}^2 = \dfrac{900}{100} = 9\ \text{cm}^2 \)
 

\(\text{Strategy 2 (convert side lengths):}\)

\(\text{Side length}\ =\sqrt{900}\ =30\ \text{mm}= \dfrac{30}{10} = 3\ \text{cm}\)

\(\text{Area} =3^2 =9\ \text{cm}^2\)

Area, SM-Bank 074 MC

A square table top has an area of 4225 square centimetres.

What is the area of the table top in square metres?

  1. \(0.4225\ \text{square metres}\)
  2. \(4.225\ \text{square metres}\)
  3. \(42.25\ \text{square metres}\)
  4. \(42\ 250\ \text{square metres}\)
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Side length}\ =\sqrt{4225} =65\ \text{cm}= \dfrac{65}{10\ 000} = 0.65\ \text{m}\)

\(\text{Area}\ =0.65^2 =0.4225\ \text{square metres}\)

\(\Rightarrow A\)

Area, SM-Bank 073 MC

A large square feature tile has an area of 15 625 square centimetres.

What is the area of the feature tile in square millimetres?

  1. \(156.25\ \text{square millimetres}\)
  2. \(1562.5\ \text{square millimetres}\)
  3. \(156\ 250\ \text{square millimetres}\)
  4. \(1\ 562\ 500\ \text{square millimetres}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Side length}\ =\sqrt{15\ 625}\ =125\ \text{cm} = 125 \times 10 = 1250\ \text{mm}\)

\(\text{Area}\ =1250^2 =1\ 562\ 500\ \text{square millimetres}\)

\(\Rightarrow D\)

Area, SM-Bank 072 MC

A square table top has an area of 9025 square centimetres.

What is the area of the table top in square millimetres?

  1. \(9.025\ \text{square millimetres}\)
  2. \(90.25\ \text{square millimetres}\)
  3. \(90\ 250\ \text{square millimetres}\)
  4. \(902\ 500\ \text{square millimetres}\)
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\(D\)

Show Worked Solution

\(\text{Side length} =\sqrt{9025} =95\ \text{cm}= 95 \times 10 = 950\ \text{mm}\)

\(\text{Area}\ =950^2 =902\ 500\ \text{square millimetres}\)

\(\Rightarrow D\)