34
Perimeter of a polygon
Textbook: Part 1, lesson 34, pp. 130–133
GoalUse the perimeter formulas of the rectangle and square and find the perimeter of composite figures.
New words
perimeter · perimetrrectangle · to‘g‘ri to‘rtburchaksquare · kvadratcomposite figure · murakkab shakl
Explanation
Opposite sides of a rectangle are equal, so for length a and width b the perimeter is P = 2(a + b) = 2a + 2b. A square with side a has perimeter P = 4a. We put the known numbers into the formula and find the unknown from an equation: if P = 50 and a = 17, then 50 = 2(17 + b), 17 + b = 25, b = 8. If the sides are given in different units, first convert them to one unit. The perimeter of a composite figure made of simple shapes is the length of its outer boundary; the sides where the shapes are joined are not counted.
Worked examples
Length 8 dm, width 12 dm: P = 2(8 + 12) = 40 dm. Sides 5 mm and 3 cm: 3 cm = 30 mm, P = 2(5 + 30) = 70 mm.
Two squares with side 3 cm joined along a side form a 6 cm × 3 cm rectangle: P = 2(6 + 3) = 18 cm (the shared side is not counted).
Class activity
“Wrapping around”: pupils build two shapes from 1 cm squares (for example 4 squares), count their perimeters and see that equal areas can have different perimeters.
Practice
1
Find the perimeter (dm) of a rectangle 13 dm long and 9 dm wide.
44
2
A rectangle has sides 5 mm and 3 cm. Find its perimeter in mm.
70
3
A rectangle has perimeter 62 cm and width 12 cm. Find its length (cm).
19
4
Why is the side where two shapes are joined not part of the perimeter of the composite figure?
It stays inside the figure, and the perimeter is only the length of the outer boundary.