Measurement and Data
Perimeter and area
Find the perimeter and the area of rectangles, squares and shapes built from them, and measure area by counting squares.
Perimeter and area answer two different questions about the same shape. Perimeter is the distance once round the outside — the length of fence you would need. Area is how much flat space is inside — the amount of grass you would have to cut. One is measured in ordinary length units, the other in square units, and mixing them up is the commonest mistake in this whole topic.
The two rules for a rectangle
Perimeter = length + width + length + width, which is quicker as 2 × (length + width). Area = length × width, because the rectangle holds that many unit squares — width rows of them, each length long. For a square both rules get simpler still, since every side is the same.
Worked example
A rectangle is 8 inches long and 5 inches wide. Find its perimeter and its area.
Perimeter: 8 + 5 + 8 + 5 = 26.
Every side is walked once. The same thing as 2 × 13.
Try it together
Now let us find the area of an L-shape together.
Start with a rectangle 10 by 4, then cut a 3 by 3 square out of one corner. Everything is measured in inches.
1.What is the area of the whole 10 by 4 rectangle, in square inches?
Have a go
Have a go on your own: a square has sides of 12 inches. What is its perimeter, in inches? Give just the number.
Hint: Four sides, all the same.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.