25
Geometry word problems
Textbook: Part 1, lesson 25, pp. 98–101
GoalUse the perimeter and area formulas of a rectangle and a square in problems.
New words
formula · formulaperimeter · perimetrarea · yuzsquare · kvadrat
Explanation
A rule written as an equality with letters is called a formula. A rectangle with width a and length b has perimeter P = 2(a + b) and area S = a · b. A square with side a has perimeter P = 4a and area S = a². Area is measured in square units: cm², dm², m². An unknown side is found with the rule for the unknown factor: b = S : a, a = P : 2 − b. In geometry problems we keep the same stages: read, plan, solve, check, and a drawing helps.
Worked examples
A rectangle is 9 cm long and its width is 4 cm less than its length: width 9 − 4 = 5 cm, area S = 9 × 5 = 45 cm², perimeter P = 2(9 + 5) = 28 cm.
A rectangle has perimeter 30 cm and width 6 cm: half the perimeter is 30 : 2 = 15, so the length is 15 − 6 = 9 cm. Check: 2(9 + 6) = 30.
Class activity
“Measuring the classroom”: groups measure the length and width of a desk, board or window with a ruler and calculate perimeter and area.
Practice
1
Find the perimeter (m) of a rectangle 12 m long and 7 m wide.
38
2
A rectangle has area 96 m² and width 8 m. Find its length (m).
12
3
A square has perimeter 52 dm. Find its side (dm).
13
4
Why is the perimeter of a rectangle given by P = 2(a + b)?
Opposite sides are equal, so the sum of the width and length is taken twice.