20
Measuring area
Textbook: pp. 72–73
GoalKnow the units of area, the area of a square and the idea of the square root.
New words
unit of area · yuz birligisquare root · kvadrat ildizare (sotix) · ar (sotix)hectare · gektar
Explanation
The unit of area is a square whose side is the unit of length: mm², cm², dm², m², km². Theorem: a square with side a has area S = a². Large fields are measured in hectares and smaller plots in ares (sotix): 1 are = 100 m², 1 ha = 100 ares = 10 000 m². If the area S of a square is known, its side is the positive number whose square is S, that is a = √S; this operation is the inverse of squaring. For example, √100 = 10 because 10² = 100. If a side of a square doubles, the area becomes 4 times as large, because (2a)² = 4a².
Worked examples
A square has perimeter 52 cm. Its side is 52 : 4 = 13 cm and its area is 13² = 169 cm².
A rectangular field is 200 m by 50 m. Its area is 10 000 m², that is 1 ha.
Class activity
“Little squares”: build 3 × 3, 4 × 4 and 5 × 5 squares from 1 cm squares, count their areas and compare with a².
Practice
1
The side of a square is 13 cm. What is its area (cm²)?
169
2
The area of a square is 144 cm². How long is a side (cm)?
12
3
A plot measures 40 m by 25 m. What is its area in ares?
10
4
Why does the area of a square become 4 times as large when its side doubles?
The new area is (2a)² = 4a², that is 4 times a².