Square millimeter. Table of units of area measurement

### 1.1. Knowledge to remember

**a) Square millimeters**

For measuring very small areas, square millimeters are also used.

- Square millimeters is the area of a square with sides 1mm long.

Square millimeter abbreviated as mm^{2.}

- We see a square of 1cm
^{2}including 100 squares of 1mm^{2}.

1cm^{2} = 100mm^{2}

1mm^{2} = cm^{2}

**b) Table of units of area measurement**

__Comment:__

– Each unit of measurement is 100 times smaller than the next smaller unit.

– Each unit of area measurement is equal to \(\frac{1}{{100}}\) the next larger unit.

### 1.2. Solve textbook exercises on pages 28 and 29

**Lesson 1 Textbook page 28**

a) Read area measurements: 29mm^{2}; 305mm^{2}; 1200mm^{2}.

b) Write the area measurements:

– One hundred and sixty-eight square millimeters

– Two thousand three hundred and ten square millimeters.

**Solution guide:**

a) 29mm^{2}: Twenty-nine square millimeters.

305mm^{2} : Three hundred and five square millimeters.

1200mm^{2}: One thousand two hundred square millimeters.

b) One hundred and sixty-eight square millimeters: 168mm^{2};

Two thousand three hundred and ten square millimeters: 2310mm^{2}.

Lesson 2 Textbook page 28

Write the correct number in the dot:

a) 5cm^{2} = … mm^{2} 1m^{2} = … cm^{2}

12km^{2} = … hm^{2} 5m^{2} = … cm^{2}

1hm^{2} = … m^{2} 12m^{2} 9dm^{2} = … dm^{2}

7hm^{2} = … m^{2} 37dam^{2} 24m^{2} = … m^{2}

b) 800mm^{2} = … cm^{2}; 3400dm^{2} = … m^{2};

12 000hm^{2} = … km^{2}; 90 000m^{2} = … hm^{2};

150cm^{2} = … dm^{2}… cm^{2}; 2010m^{2} = … dam^{2}… m^{2}

__Solution guide:__

a) 5cm2 = 500 mm2 1m2 = 10 000 cm2

12km2 = 1200 hm2 5m2 = 50 000 cm2

1hm2 = 10 000 m2 12m2 9dm2 = 1209 dm2

7hm2 = 70 000 m2 37dam2 24m2 = 3724 m2

b) 800mm2 = 8 cm2; 3400dm2 = 34 m2;

12 000hm2 = 120 km2; 90 000m2 = 9 hm2;

150cm2 = 1 dm2 50 cm2; 2010m2 = 20 dam210 m2

Lesson 3 Textbook page 28

Write the appropriate fraction in the mark: (CTGT omitted this post. Abbreviated CTGT omitted)

a) 1mm2 = … cm2 b) 1dm2 = … m2

8mm2 = … cm2 7dm2 = … m2

29mm2 = … cm2 34dm2 = … m2

__Solution guide:__

a) 1mm2 = \(\frac{1}{{100}}\) cm2 b) 1dm2 = \(\frac{1}{{100}}\) m2

8mm2 = \(\frac{8}{{100}}\) cm2 7dm2 = \(\frac{7}{{100}}\) m2

29mm2 = \(\frac{29}{{100}}\) cm2 34dm2 = \(\frac{34}{{100}}\) m2

### 1.3. Solve the exercises in the textbook Practice pages 28, 29

**Lesson 1 of the textbook page 28:**

a) Write the following measurements as square meters:

6m^{2} 35dm^{2}; 8m^{2} 27dm^{2}; 16m^{2} 9dm^{2}; 26dm^{2}.

Model: 6m^{2} 35dm^{2} = 6m^{2} + \(\frac{{35}}{{100}}\) m^{2} = \(6\frac{{35}}{{100}}\) m^{2}.

b) Write the following numbers as measurements in square decimeters:

4dm^{2} 65cm^{2}; 95cm^{2}; 102dm^{2} 8cm^{2}.

*Solution guide:*

a)

8m2 27dm2 = 8m2 + \(\frac{{27}}{{100}}\) m2 = \(8\frac{{27}}{{100}}\) m2.

16m2 9dm2 = 16m2 + \(\frac{{9}}{{100}}\) m2 = \(16\frac{{9}}{{100}}\) m2.

\(26d{m^2} = \frac{{26}}{{100}}{m^2}\)

b)

4dm^{2} 65cm^{2} = 4dm^{2} + \(\frac{{65}}{{100}}\) dm^{2} = \(4\frac{{65}}{{100}}\) dm^{2}

95cm^{2} = \(\frac{{95}}{{100}}\) dm^{2}

102dm^{2} 8cm^{2} = 102dm^{2} + \(\frac{{8}}{{100}}\) dm^{2} = \(102\frac{{8}}{{100}}\) dm^{2}

Lesson 2 Textbook page 28:

Choose a letter that has a right answer:

3cm^{2} 5mm^{2} = … mm^{2}

The correct number to write in the dot is:

A. 35 B. 305

C. 350 D. 3500

*Solution guide:*

We have: 3cm^{2 }5mm^{2 }= 3cm^{2 }+ 5mm^{2 }= 300mm^{2 } + 5mm^{2 } = 305mm^{2 }

So 3cm^{2 }5mm^{2 }= 305 mm^{2 }

Choose B.

Lesson 3 Textbook page 29:

Fill in the blanks with > , < or = :

2dm^{2} 7cm^{2} … 207cm^{2} 300mm^{2} … 2cm^{2} 89mm^{2}

3m^{2} 48 dm^{2} … 4m^{2} 61 km^{2} … 610hm^{2}

*Solution guide:*

- 2dm
^{2}7cm^{2}=2dm^{2}+ 7cm^{2}= 200cm^{2}+ 7cm^{2}= 207cm^{2}

So: 2dm^{2} 7cm^{2} = 207cm^{2}

- 3m
^{2}48dm^{2}= 348dm^{2}; 4m^{2}= 400dm^{2}; which 348 dm^{2}< 400dm^{2}

So: 3m^{2} 48dm^{2} < 4m^{2}

- 2cm
^{2}89mm^{2}= 289mm^{2}; which 300mm^{2}> 289mm^{2}

So: 300mm^{2} > 2cm^{2} 89mm^{2}

- 61km
^{2}= 6100hm^{2}; that 6100hm^{2}> 610hm^{2}

So: 61km^{2} > 610hm^{2}

Lesson 4 Textbook page 29:

To pave the floor of a room, people have used 150 square bricks with side 40cm. How many square meters is the red room, knowing the area of the grout circuit is negligible?

*Solution guide:*

The area of a brick is:

40 × 40 = 1600 (cm^{2})

Room size is:

1600 × 150 = 240000 (cm^{2}) = 24m^{2}

Answer: 24m^{2}

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