86
Total edge length of a cuboid
Textbook: Part 3, lesson 86, pp. 56–57
GoalThe total length of all edges of a cuboid: L = a × 4 + b × 4 + c × 4.
New words
length · bo‘yiwidth · eniheight · balandligitube, rod · naycha
Explanation
A cuboid has 12 edges: four of length a, four of width b and four of height c. The total length of all edges is L = a × 4 + b × 4 + c × 4 = (a + b + c) × 4. For a cube a = b = c, so L = a × 12.
Worked examples
a = 9 cm, b = 6 cm, c = 4 cm: L = (9 + 6 + 4) × 4 = 19 × 4 = 76 cm.
Length 8 dm, width 5 dm, height 2 dm: L = (8 + 5 + 2) × 4 = 60 dm.
Class activity
“Building a frame”: groups take four sticks of each of three different lengths, build a cuboid and work out the total length.
Practice
1
A cuboid is 10 cm long, 7 cm wide and 3 cm high. What is the total length of its edges in cm?
80
2
A cuboid is 14 cm long, 9 cm wide and 2 cm high. What is the total length of its edges in cm?
100
3
For a frame, four rods of 12 cm, four of 9 cm and four of 5 cm were taken. What is the total length of the rods in cm?
104
4
A cuboid has a square base with side 8 cm and height 15 cm. What is the total length of its edges in cm?
124
5
The edges of a cuboid total 96 cm; its length is 15 cm and width 5 cm. How many centimetres is its height?
4