Formulas
One rule with letter-numbers that works for every case.
Perimeter of a square
The perimeter of a square is the distance around it. It is 4 times the length of its side.
A square has sides of 5 cm. Another has sides of 9 cm. Is there one rule that gives the perimeter of every square?
What this lesson covers
The idea
A general mathematical relation expressed using letter-numbers is called a formula.
Perimeter of a square
The perimeter of a square is the distance around it. It is 4 times the length of its side.
A square has sides of 5 cm. Another has sides of 9 cm. Is there one rule that gives the perimeter of every square?
- No. Each square needs its own rule.
- Yes: 4 times the side.
- Yes: the side plus 4.
Squares of every size
Let the letter q stand for the side. Change *q* and watch the perimeter. Then try other shapes.
One rule for every size
P = 4 × q is true for every square: put any side in place of *q* and it gives the perimeter. Other shapes have rules of their own.
A general mathematical relation expressed using letter-numbers is called a formula.
- Shape | Side | Rule
- Square | q | P = 4 × q
- Equilateral triangle | t | P = 3 × t
- Regular hexagon | h | P = 6 × h
Notes
A general mathematical relation expressed using letter-numbers is a formula: P = 4 × q gives the perimeter of every square.
Check yourself
Use the formula P = 4 × q for a square with side 8 cm. What is the perimeter?
Answer: 32 cm
P = 4 × 8 = 32 cm.
A regular hexagon has the formula P = 6 × h. What is its perimeter when *h* is 7 cm?
Answer: 42 cm
P = 6 × 7 = 42 cm.
Which of these is a formula?
A square has a perimeter of 40 cm. Using P = 4 × q, what is its side?
Answer: 10 cm
4 × 10 = 40, so the side is 10 cm.
- 4 × 5 = 20, the perimeter of one square. That is true for one square only. A formula works for all.
- The number 20. A single number is not a relation between quantities.
- P = 4 × q, which gives the perimeter of any square — correct. Yes! It is a general relation written with letter-numbers.