An area of 12 can be 1 by 12, 2 by 6, or 3 by 4. All have area 12.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
But different perimeters
1 by 12 has perimeter 26. 3 by 4 has perimeter 14. Very different.
The squarest is the shortest
The rectangle closest to a square has the smallest perimeter.
Many rectangles, one area
Area 36 can be made as 1 × 36, 2 × 18, 3 × 12, 4 × 9, or 6 × 6. All five hold the same amount of surface and look completely different. Finding them all is really finding all the ways 36 can be written as a product — a first look at factors.
The perimeters are not the same
The 1 × 36 rectangle has perimeter 74; the 6 × 6 square has perimeter 24. Long thin shapes have far more edge for the same amount of inside. The squarest rectangle always has the smallest perimeter, which is a genuinely surprising and useful fact.
Why this matters outside maths
A farmer with a fixed length of fence gets the most land by making the field as square as possible. A packaging designer wants the least card for a given volume. Choosing between shapes with the same area is a real decision, not a puzzle invented for school.
Step 2: Try It Yourself
Tap and try it out.
Area · squares inside
12
Perimeter · walk around
14
3 × 4 = 12 · 3 + 4 + 3 + 4 = 14
Area counts the squares inside. Perimeter measures the walk all the way round.
Step 3: Watch an Example
One step at a time.
Watch Ana Try Every Rectangle
Ana looks for rectangles with an area of 12.
- Step 1
She lists the factor pairs of 12: 1 and 12, 2 and 6, 3 and 4.
Step 4: Your Turn
Practice makes it stick.
The Pen
Problem 1 of 2
A pen with area 16 can be 4 by 4 or 2 by 8. Which needs less fence?
The Long One
Problem 2 of 2
A rectangle 1 by 12. What is its perimeter?
units
Same Area, Different Shape
1 of 3
A 2 by 6 rectangle. What is its perimeter?
2 of 3
A 3 by 4 rectangle. What is its perimeter?
3 of 3
Both have area 12. Do they have the same perimeter?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A 2 by 9 rectangle. What is its area?
Question 2 of 2
Which rectangle with area 36 has the smallest perimeter?
What You Learned
- Rectangles with the same area can have different shapes.
- They can have very different perimeters.
- The squarest rectangle has the smallest perimeter.