Area & perimeter puzzles, step by step
Finding a rectangle's area is one step.
How long are its two sides?
Two facts, and only one pair fits both
- Two numbers are given and neither of them is a side: an area of 24 and a perimeter of 28. Both were worked out FROM the sides, and the job is to go back the other way.
- Deal with the perimeter first, because it counts every side twice. Going right round is two long sides and two short ones, so half of it is one of each: 28 ÷ 2 = 14. The two sides add to 14.
- Now use the area to write out the possibilities. These are all the ways two whole numbers multiply to 24 — 4 of them, and every one is a rectangle with exactly the right area. The area alone cannot choose between them.
- So go down the list adding each pair, and stop where the total is 14: 2 + 12 = 14. That is the only pair that fits BOTH facts, which is what makes it the answer rather than an answer.
How it works.
- 01
Two numbers are given and neither of them is a side: an area of 24 and a perimeter of 28. Both were worked out FROM the sides, and the job is to go back the other way.
- 02
Deal with the perimeter first, because it counts every side twice. Going right round is two long sides and two short ones, so half of it is one of each: 28 ÷ 2 = 14. The two sides add to 14.
- 03
Now use the area to write out the possibilities. These are all the ways two whole numbers multiply to 24 — 4 of them, and every one is a rectangle with exactly the right area. The area alone cannot choose between them.
- 04
So go down the list adding each pair, and stop where the total is 14: 2 + 12 = 14. That is the only pair that fits BOTH facts, which is what makes it the answer rather than an answer.