21
Area of a rectangle
Textbook: pp. 74–76
GoalKnow the formula for the area of a rectangle and use it in problems.
New words
area of a rectangle · to‘g‘ri to‘rtburchak yuzilength and width · bo‘yi va eniadjacent sides · qo‘shni tomonlarperimeter · perimetr
Explanation
Theorem: the area of a rectangle with sides a and b is S = a · b, the product of its adjacent sides. Proof: cut a square of side a + b into squares of sides a and b and two equal rectangles. Adding areas, (a + b)² = a² + 2S + b², so 2S = 2ab and S = ab. From the formula the other side is b = S : a. The perimeter P = 2(a + b) must not be confused with the area, because they are different quantities. If both sides double, the area becomes four times as large.
Worked examples
A rectangle has area 96 cm² and one side 8 cm. The other side is 96 : 8 = 12 cm.
A rectangle has perimeter 28 cm and is 4 cm longer than wide. 2(x + x + 4) = 28, x = 5; the sides are 5 cm and 9 cm and the area is 45 cm².
Class activity
“Area of a room”: measure the sides of your classroom or a desk with a tape and calculate its area.
Practice
1
The sides of a rectangle are 9 cm and 14 cm. What is its area (cm²)?
126
2
A rectangle has area 84 cm² and one side 7 cm. How long is the other side (cm)?
12
3
A rectangle has perimeter 30 cm and width 6 cm. What is its area (cm²)?
54
4
Why does the area of a rectangle become 4 times as large when both sides double?
The new area is 2a · 2b = 4ab, which is 4 times the old one.