Faces and Edges of Cuboids
Semester 4B · Chapter 17 · Lesson 3 · MATH-4B-C17-L03
Before you begin: prerequisite check
Recall: 17.01–17.02. Attempt these questions independently first.
A cuboid measures 3 cm by 6 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid measures 6 cm by 2 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Draw one connected, foldable six-face net of a 3 cm by 2 cm by 5 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Key vocabulary
- cuboid
- solid with six rectangular faces
- face
- flat rectangular side of a cuboid
- edge
- segment where two faces meet
- vertex
- point where edges meet
- net
- connected plane arrangement of faces that folds into a solid
Understand the concept
In a cuboid, there are four edges of each of the three side lengths. For dimensions 2, 3, and 4 centimeters, the combined length of all twelve edges is 4×(2+3+4)=36 centimeters. Each rectangular face has dimensions chosen from a pair of those lengths. Opposite faces are congruent; opposite edges on any face are equal. Use a labeled sketch to explain which groups of edges you are counting and avoid confusing total edge length with volume or surface area.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
A cuboid has side lengths 6 cm, 3 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(6+3+5)=56 cm.
Check 1: try it yourself
A cuboid has side lengths 4 cm, 7 cm and 5 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+7+5)=64 cm.
Worked example 2
A cuboid has side lengths 5 cm, 8 cm and 9 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(5+8+9)=88 cm.
Check 2: try it yourself
A cuboid has side lengths 5 cm, 5 cm and 5 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(5+5+5)=60 cm.
Worked example 3
A cuboid has side lengths 3 cm, 6 cm and 5 cm. Find the combined length of all twelve edges.
There are four of each dimension. Total = 4×(3+6+5)=56 cm.
Check 3: try it yourself
A cuboid has side lengths 4 cm, 6 cm and 6 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+6+6)=64 cm.
Guided practice
A cuboid has side lengths 4 cm, 4 cm and 7 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+4+7)=60 cm.
A cuboid has side lengths 2 cm, 8 cm and 8 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(2+8+8)=72 cm.
A cuboid has side lengths 5 cm, 4 cm and 6 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(5+4+6)=60 cm.
A cuboid has side lengths 6 cm, 6 cm and 4 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(6+6+4)=64 cm.
A cuboid has side lengths 5 cm, 6 cm and 7 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(5+6+7)=72 cm.
Independent practice
A cuboid has side lengths 7 cm, 4 cm and 9 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(7+4+9)=80 cm.
A cuboid has side lengths 7 cm, 8 cm and 8 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(7+8+8)=92 cm.
A cuboid has side lengths 7 cm, 5 cm and 9 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(7+5+9)=84 cm.
A cuboid has side lengths 4 cm, 3 cm and 6 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+3+6)=52 cm.
A cuboid has side lengths 7 cm, 8 cm and 7 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(7+8+7)=88 cm.
A cuboid has side lengths 4 cm, 5 cm and 6 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+5+6)=60 cm.
A cuboid has side lengths 2 cm, 7 cm and 5 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(2+7+5)=56 cm.
A cuboid has side lengths 4 cm, 3 cm and 4 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+3+4)=44 cm.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
A cuboid has side lengths 6 cm, 5 cm and 4 cm. Find the combined length of all twelve edges. Explain or sketch the mathematical relationship.
Show answer and reasoning
There are four of each dimension. Total = 4×(6+5+4)=60 cm. State which quantities or geometric properties justify the method.
A learner claims: “All six faces of a cuboid must be equal squares.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: a cuboid has three pairs of equal rectangles; all six square faces occur only for the special case of a cube. Explain the relevant quantities or properties, not merely the final answer.
Exit check
A cuboid has side lengths 4 cm, 6 cm and 5 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(4+6+5)=60 cm.
A cuboid has side lengths 6 cm, 5 cm and 6 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(6+5+6)=68 cm.
A cuboid has side lengths 5 cm, 7 cm and 9 cm. Find the combined length of all twelve edges.
Show answer and reasoning
There are four of each dimension. Total = 4×(5+7+9)=84 cm.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.