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Measuring area
The need to measure area dates back to ancient times. Due to the periodic flooding of the Nile in Ancient Egypt, landowners had to mark the border of their lands again year after year.
Areas to be measured can be compared to squares.
The basic unit of area is \latex{ 1 } \latex{square} \latex{ metre } (\latex{ m^{2}}). It is the area of a square with sides that are \latex{ 1 } \latex{ m } long.
Smaller units of area are shown below.
area of a square with sides measuring \latex{ 1 } \latex{ mm } in length:
area of a square with sides measuring \latex{ 1 } \latex{ cm } in length:
area of a square with sides measuring \latex{ 1 } \latex{ dm } in length:
\latex{ 1 } \latex{ mm^{2} }
\latex{ 1 } \latex{ cm^{2} }
\latex{ 1 } \latex{ dm^2 }
\latex{ 1 } \latex{ cm^{2} }
\latex{ 1 } \latex{ dm^{2} }
The size of flats is usually measured in \latex{ square } \latex{ metres }, that of land in \latex{ hectares } and the area of countries in \latex{ square } \latex{ kilometres }.
The units of area:
length of the side of the square
area of the square
name of the unit
\latex{ 1 } \latex{ mm }
\latex{ 1 } \latex{ cm }
\latex{ 1 } \latex{ dm }
\latex{ 1 } \latex{ m }
\latex{ 10 } \latex{ m }
\latex{ 100 } \latex{ m }
\latex{ 1 } \latex{ km }
\latex{ 1 } \latex{ mm^{2} }
\latex{ 1 } \latex{ cm^{2} }
\latex{ 1 } \latex{ dm^{2} }
\latex{ 1 } \latex{ m^{2} }
\latex{ 100 } \latex{ m^{2} }
\latex{ 10,000 } \latex{ m^{2} }
\latex{ 1 } \latex{ km^{2} }
\latex{ square } \latex{ millimetre }
\latex{ square } \latex{ centimetre }
\latex{ square } \latex{ decimetre }
\latex{ square } \latex{ metre }
\latex{ are (a) }
\latex{ hectare (ha) }
\latex{ square } \latex{ kilometre }
area
\latex{ 1 }
\latex{ m^{2} }
value
unit
\latex{1}
\latex{1}
\latex{1}
\latex{1}
\latex{1}
\latex{1}
\latex{1}
<
<
<
<
<
<
\latex{\times 100}
\latex{\times 100}
\latex{\times 100}
\latex{\times 100}
\latex{\times 100}
\latex{\times 100}
\latex{100\; {mm}^2 = 1\;{cm}^2}
\latex{100\; {dm}^2 = 1\;{m}^2}
\latex{100\; {a} = 1\;{ha}}
\latex{100\; {cm}^2 = 1\;{dm}^2}
\latex{100\; {m}^2 = 1\;{a}}
\latex{100\; {ha} = 1\;{km}^2}
\latex{1\; {m}^2 = 100\;{dm}^2 = 10,000 \; {cm}^2 = 1 \; {m}^2 = 1,000,000 \; {mm}^2}
\latex{1\;{km}^2 = 100\; {ha} = 10,000 \; {a} = 1,000,000 \; {m}^2 }
\latex{ mm^{2} }
\latex{cm^{2} }
\latex{dm^{2} }
\latex{m^{2} }
\latex{a}
\latex{ha}
\latex{km^{2} }
Exercises
{{exercise_number}}. Estimate the area of the
a) classroom
b) school courtyard
c) football field of the school
d) maths book
e) sole of a shoe
f) side of a €\latex{ 1 } coin
You can use different units.
{{exercise_number}}. The ant can measure only in \latex{ square } \latex{ millimetres }, the mouse in \latex{ square } \latex{ centimetres }, the rabbit in \latex{ square } \latex{ decimetres }, and the elephant in \latex{ square } \latex{ metres }. Convert the following quantities into their units.
a) \latex{ 21 } \latex{ cm^{2} }
b) \latex{ 523 } \latex{ cm^{2} }
c) \latex{ 6 } \latex{ m^{2} } \latex{ 2 } \latex{ cm^{2} }
d) \latex{ 48 } \latex{ m^{2} } \latex{ 518 } \latex{ mm^{2} }
b) \latex{ 523 } \latex{ cm^{2} }
c) \latex{ 6 } \latex{ m^{2} } \latex{ 2 } \latex{ cm^{2} }
d) \latex{ 48 } \latex{ m^{2} } \latex{ 518 } \latex{ mm^{2} }
a) \latex{ 43,000 } \latex{ mm^{2} }
b) \latex{ 45 } \latex{ cm^{2} } \latex{ 1,200 } \latex{ mm^{2} }
c) \latex{ 6 } \latex{ m^{2} } \latex{ 2,500 } \latex{ mm^{2} }
d) \latex{ 21 } \latex{ m^{2} } \latex{ 6,300 } \latex{ mm^{2} }
b) \latex{ 45 } \latex{ cm^{2} } \latex{ 1,200 } \latex{ mm^{2} }
c) \latex{ 6 } \latex{ m^{2} } \latex{ 2,500 } \latex{ mm^{2} }
d) \latex{ 21 } \latex{ m^{2} } \latex{ 6,300 } \latex{ mm^{2} }
a) \latex{ 540,000 } \latex{ mm^{2} }
b) \latex{ 6 } \latex{ m^{2} } \latex{ 23 } \latex{ dm^{2} }
c) \latex{ 5 } \latex{ m^{2} } \latex{ 23,000 } \latex{ cm^{2} }
d) \latex{ 49 } \latex{ m^{2} } \latex{ 86,000 } \latex{ cm^{2} }
b) \latex{ 6 } \latex{ m^{2} } \latex{ 23 } \latex{ dm^{2} }
c) \latex{ 5 } \latex{ m^{2} } \latex{ 23,000 } \latex{ cm^{2} }
d) \latex{ 49 } \latex{ m^{2} } \latex{ 86,000 } \latex{ cm^{2} }
a) \latex{ 8 } \latex{ km^{2} }
b) \latex{ 250,000 } \latex{ cm^{2} }
c) \latex{ 3,700,000 } \latex{ cm^{2} }
d) \latex{ 9 } \latex{ m^{2} } \latex{ 70,000 } \latex{ cm^{2} }
b) \latex{ 250,000 } \latex{ cm^{2} }
c) \latex{ 3,700,000 } \latex{ cm^{2} }
d) \latex{ 9 } \latex{ m^{2} } \latex{ 70,000 } \latex{ cm^{2} }
{{exercise_number}}. Which one is greater?
a) \latex{ 4 } \latex{ km^{2} } or \latex{ 58,000 } \latex{ m^{2} }
b) \latex{ 16 } \latex{\large a } or \latex{ 2,300 } \latex{ m^{2} }
c) \latex{ 245 } \latex{ mm^{2} } or \latex{ 1 } \latex{ cm^{2 }} \latex{ 168 } \latex{ mm^{2} }
d) \latex{ 78 } \latex{ cm^{2} } \latex{ 259 } \latex{ mm^{2} } or \latex{ 8,000 } \latex{ mm^{2} }
{{exercise_number}}. Choose the most probable answer.
a) The area of an A\latex{ 4 } paper sheet: \latex{ 60 } \latex{ mm^{2} }; \latex{ 600 } \latex{ cm^{2} }; \latex{ 6 } \latex{ m^{2} }.
b) The area of a room: \latex{ 12 } \latex{ mm^{2} }; \latex{ 28 } \latex{ km^{2} }; \latex{ 16 } \latex{ m^{2} }.
c) The area of a table: \latex{ 32 } \latex{ km^{2} }; \latex{ 2 } \latex{ m^{2} }; \latex{ 45 } \latex{ mm^{2} }.
d) The area of a TV screen: \latex{ 1,500 } \latex{ cm^{2} }; \latex{ 15 } \latex{ m^{2} }; \latex{ 150 } \latex{ km^{2} }.
e) The cross-section of the point of a pencil: quarter of a \latex{ mm^{2} }; \latex{ 3 } \latex{ cm^{2} }; half a \latex{ m^{2} }.
f) The area of a forest: \latex{ 100 } \latex{ m^{2} }; \latex{ 100 } \latex{ cm^{2} }; \latex{ 100 } \latex{ ha }.
b) The area of a room: \latex{ 12 } \latex{ mm^{2} }; \latex{ 28 } \latex{ km^{2} }; \latex{ 16 } \latex{ m^{2} }.
c) The area of a table: \latex{ 32 } \latex{ km^{2} }; \latex{ 2 } \latex{ m^{2} }; \latex{ 45 } \latex{ mm^{2} }.
d) The area of a TV screen: \latex{ 1,500 } \latex{ cm^{2} }; \latex{ 15 } \latex{ m^{2} }; \latex{ 150 } \latex{ km^{2} }.
e) The cross-section of the point of a pencil: quarter of a \latex{ mm^{2} }; \latex{ 3 } \latex{ cm^{2} }; half a \latex{ m^{2} }.
f) The area of a forest: \latex{ 100 } \latex{ m^{2} }; \latex{ 100 } \latex{ cm^{2} }; \latex{ 100 } \latex{ ha }.
{{exercise_number}}. Arrange the following countries in ascending order according to their area. (Find the necessary data on the Internet or in your atlas or make an estimation.)
Malta; France; Germany; United Kingdom; Austria.
{{exercise_number}}.
a) What is the area of the yellow figures if the area of the red square is \latex{ 1 } \latex{ cm^{2}?}
b) How many \latex{ square } \latex{ centimetres } is the area of the yellow figures if the area of the red square is \latex{ 2 } \latex{ cm^{2} ?}
b) How many \latex{ square } \latex{ centimetres } is the area of the yellow figures if the area of the red square is \latex{ 2 } \latex{ cm^{2} ?}
\latex{ A })
\latex{ B })
\latex{ C })
\latex{ D })
\latex{ E })
\latex{ F })
\latex{ G })
{{exercise_number}}. Draw figures on quad paper whose area is
a) \latex{ 8 } squares;
b) \latex{ 12 } squares;
c) \latex{ 9 } squares;
d) \latex{ 16 } squares;
e) \latex{ 4 } and a half squares;
f) \latex{ 10 } and a half squares.
{{exercise_number}}. How many \latex{ square } \latex{ millimetres } is the area of the yellow figures if the area of the red triangle is \latex{ 3 } \latex{ cm^{2} ?}
\latex{ A })
\latex{ B })
\latex{ C })
\latex{ D })
\latex{ E })
\latex{ F })
\latex{ G })
{{exercise_number}}. How many \latex{ square } \latex{ centimetres } is the area of the yellow figures if the area of the red hexagon is \latex{ 18 } \latex{ cm^{2} ?}
\latex{ A })
\latex{ B })
\latex{ C })
\latex{ D })
{{exercise_number}}. What fraction of the following shapes is red?
\latex{ A })
\latex{ B })
\latex{ C })
\latex{ D })
\latex{ E })
{{exercise_number}}. Estimate the area of each leaf. (→)
\latex{ A })
\latex{ B})
{{exercise_number}}. Use five squares with sides measuring \latex{ 1 } \latex{ cm } in length to create various shapes. Always accurately align the sides of two squares, and use all five squares for each shape. Create as many shapes as possible. Count the number of square sides bordering each shape.
Quiz
Find a method to determine which shape has a larger area.
\latex{ A })
\latex{ B })
