Perimeter and Area
Perimeter is the distance around; area is the space inside.
About this topic
Perimeter is the distance around a shape, measured in length units such as metres, while area is the amount of surface inside, measured in square units. Rectangle: P = 2(l + w), A = lw. Triangle: A = ½bh. Parallelogram: A = bh.
Shapes with the same perimeter can have very different areas. Fencing a garden needs perimeter, but buying paint or turf needs area. Splitting complicated shapes into simple ones is a handy strategy.
Worked example: a rectangular garden is 10 m by 6 m. Its perimeter is 2(10 + 6) = 32 m of fencing, and its area is 60 square metres. A 8 by 8 square also has a perimeter of 32 but an area of 64, bigger. A long thin 15 by 1 rectangle has the same perimeter and an area of only 15. For an L-shaped room, split it into two rectangles and add their areas.
Contractors price paint by area and baseboards by perimeter. A very common mistake is mixing units: perimeter uses plain length units, area uses square units, and converting 1 square metre to centimetres gives 10,000 square centimetres, not 100. Another is adding all numbers in a problem without deciding what is needed. Draw a diagram and label the dimensions. For a given perimeter, the square has the greatest area among rectangles.
Key ideas
- Rectangle area = l × w
- Perimeter adds all sides
- Area is measured in square units
Quick check
Use cases: where Perimeter and Area helps
- Homework: review the key idea behind Perimeter and Area before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Perimeter and Area without notes.
- Visual learning: play with the interactive lab to see how Perimeter and Area changes when you adjust its inputs.
- Teaching a friend: explain Perimeter and Area in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Perimeter and Area?
Perimeter is the distance around; area is the space inside.
What will I learn in Perimeter and Area?
Rectangle area = l × w. Perimeter adds all sides. Area is measured in square units.
Is Perimeter and Area part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Perimeter and Area lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Perimeter and Area?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.