36
Area of a rectangle
Textbook: Part 1, lesson 36, pp. 136–140
GoalKnow the area of a figure and units of area; find the area of a rectangle and square by formula; the square root.
New words
area · yuzsquare centimetre · kvadrat santimetrsquare root · kvadrat ildizunit square · birlik kvadrat
Explanation
Finding the area of a figure means finding how many unit squares cover it. The unit square has side 1 mm, 1 cm, 1 dm or 1 m; area is measured in mm², cm², dm², m². A rectangle with width a and length b has area S = a · b; a square with side a has area S = a². If the sides are in different units, first convert them to one unit. To find the side of a square from its area we need the number which, multiplied by itself, gives that area; it is called the square root: √49 = 7 because 7² = 49. By definition (√a)² = a.
Worked examples
A room floor 7 m by 12 m: S = 7 × 12 = 84 m². A square with area 169 cm² has side √169 = 13 cm because 13² = 169.
Sides 2 m and 150 cm: 2 m = 200 cm, S = 200 × 150 = 30 000 cm². A square of side 12 cm: S = 12² = 144 cm².
Class activity
“Area of a page”: pupils count notebook squares to estimate the area of a page, then measure and check with the formula.
Practice
1
Find the area (cm²) of a rectangle 14 cm long and 9 cm wide.
126
2
Find in cm² the area of a rectangle with sides 2 m and 150 cm.
30000
3
How many metres is the side of a square with area 196 m²?
14
4
Why do we convert the sides to one unit before finding the area?
The unit square must be one definite square: multiplying m by cm gives an answer in no proper unit.