1:Measuring Area: Precise discussion

Measuring Area is finding the quantity that expresses the extent of a given surface on a plane. It is a derived quantity of length. Area is obtained from product of two lengths. The SI Unit of area is square meter (m²).

square meter can be expressed into other units like square-centimeter (cm²), square-millimeter(mm²) or square-kilometer (km²).

1 m² = 1m x 1m

but 1m = 100cm

hence 1m² =100cm x 100cm

and so 1m² =10000cm²

similarly;

1m = 1000mm (millimeters)

1m² =1000mm x 1000mm =1000,000 mm².

1 km² =1000m x 1000m = 1000,000 m².

we will go ahead and convert area in square meters to some other units.

Example: converting area from square centimeters to square-meters

Express the following into square-centimeter (cm²)

1. 8.2 m²
2. 5.4 m²
3. 0.078m²
4. 0.000000000064 km²

solution

1.     1m² =100cm x 100cm=10000cm²  

     1m² =10000cm²

      8.2m = ?

2. 

1m² =100cm x 100cm=10000cm²

1m² =10000cm²

5.4=?

3.

1m² =100cm x 100cm=10000cm²

1m² =10000cm²

0.078=?

4.

1km² =1000m x 1000m=1000 x 100 cm x 1000 x 100 cm

1km² =10,000,000,000cm²

0.000000000064 km² = ?

Example problem converting square-metre to square centimeter

convert the following into m²

1. 4500 cm²
2. 0.0072 cm²

solution

1.

1m² = 10000cm²

? = 4500cm²

2.

1m² = 10000cm²

? = 0.0072 cm²

Area of irregularly-shaped surfaces

Irregular shapes are shapes that cannot be precisely described in terms of geometrical shapes. Their edges and vertices are not uniform.

An estimate of the area of an irregular shape can be made by dividing the shape up into squares each of area 1 cm² . By counting the number of small squares, the area of the irregular shape can be estimated. consider the diagram below.

in the figure above, the number of squares that are completely covered by the shape are 39. The number of squares that have been touched by the figure (partially covered) are 30. confirm by counting.

The area is thus calculated as follow:

Area covered by complete squares = 39 cm² .

Area covered by partially covered squares = 30/2= 15cm² .

Therefore the area covered by the figure =( 39 + 15 ) cm²=54 cm²

Hence the estimated area of the given figure is 54 cm²

Exercise: Measuring Area

Determine the area of the figure below.

Example 2: Find the area of the irregular surface shown:

Related pages

• Physical Quantities
• Length
• Reading a meter rule
• Measuring with a meter rule
• Area
• Area of irregularly shaped surfaces
• Volume
• Volume of regularly shaped objects
• Measuring volume of liquids
• Volume of irregular solids
• Measuring Mass
• Density
• Densities of some substances
• Questions on Measurements
• Reading meter Rule with accuracy
• Using metre rule

---