40
Chapter IV review problems
Textbook: Part 2, lesson 40, pp. 15–17
GoalReview Chapter IV: angles, perimeter, area, units of area.
New words
perimeter · perimetrarea · yuzhectare · gektarapproximate area · taqribiy yuz
Explanation
For a rectangle P = 2(a + b) and S = a · b; for a square P = 4a and S = a². Before finding the area, convert the sides to one unit. Units of area differ by a factor of 100: 1 m² = 100 dm² = 10 000 cm², 1 ar = 100 m², 1 ha = 100 ar = 10 000 m². The area of a composite figure is found by adding its parts or by completing it and subtracting the extra. The area of a right triangle is half the area of the matching rectangle. The area of a curved figure is estimated with a grid.
Worked examples
A rectangle with sides 8 cm and 5 cm: P = 2(8 + 5) = 26 cm, S = 8 × 5 = 40 cm². Perimeter is in length units, area in square units.
If a 3 × 2 cm piece is cut from a 9 × 7 cm rectangle, the area is 9 × 7 − 3 × 2 = 63 − 6 = 57 cm².
Class activity
“Area or perimeter?”: the teacher shows cards (“wire for a fence”, “tiles for a floor”, “paint”, etc.); pupils say whether perimeter or area is needed.
Practice
1
Find in dm² the area of a rectangle 14 dm long and 230 cm wide.
322
2
A plot is 125 m × 96 m. Find its area in ar.
120
3
A square sheet of side 3 m is cut into squares of side 1 dm. How many pieces are there?
900
4
Why is 1 ha = 10 000 m²?
1 ha is a square with side 100 m: 100 m × 100 m = 10 000 m².