Perimeter — Grade 7 Accelerated, what it means and where it is taught
Distance all the way around the outside.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Circumference — The perimeter of a circle: C = 2π r.
Practise this idea
22 questions in the course bank use Perimeter, in Reasoning with Equations & Inequalities, Proportional Reasoning with Scale Drawings, Length and Area in 2-D Figures, Measurement, Circles, Congruence & Sequences of Transformations. The first 8 are below; the rest are in those units.
Problem 1
A rectangle's length is 3 more than its width, and its perimeter is 26. Find the width.
Worked answer
5
2w + 2(w + 3) = 26
4w + 6 = 26
4w = 20, so w = 5 and the length is 8 ✓
Problem 2
Triangle ABC has sides 6, 8, 10. A similar triangle has shortest side 9. Find its perimeter.
Worked answer
36
k = 96 = 1.5
Sides become 9, 12, 15
Perimeter = 36. (Or 24 × 1.5 = 36.)
Problem 3
Two similar figures have areas 25 cm2 and 64 cm2. The smaller has perimeter 20 cm. Find the larger perimeter.
Worked answer
32
k2 = 6425, so k = 85
Perimeter is a length, so it scales by k
20 × 85 = 32 cm
Problem 4
A rectangle has perimeter 30 and length 9. Find its width.
Worked answer
6
18 + 2w = 30
2w = 12
w = 6
Problem 5
Among rectangles with whole-number sides and perimeter 24, which has the greatest area?
- 1 × 11
- 3 × 9
- 4 × 8
- 6 × 6
Worked answer
6 × 6
Areas: 11, 27, 32, 36
The square wins. For a fixed perimeter, the closer to square, the larger the area.
Problem 6
Find the perimeter of a 7 cm by 4 cm rectangle.
Worked answer
22
2(7 + 4) = 22 cm
Problem 7
A rectangle has perimeter 36 and length 11. Find its width.
Worked answer
7
22 + 2w = 36
2w = 14, so w = 7
Problem 8
A shape is a 20 m by 14 m rectangle with a semicircle of diameter 14 m on each short end. Find the perimeter. Use π ≈ 3.14.
Worked answer
83.96
The two semicircles form one circle: C = 3.14 × 14 = 43.96 m
The two long sides: 20 + 20 = 40 m
43.96 + 40 = 83.96 m