What is this skill?
Perimeter is the distance all the way around the outside of a shape. To find it, you add the lengths of all the sides. A rectangle 7 inches long and 4 inches wide has a perimeter of 7 + 4 + 7 + 4 = 22 inches. Third graders find perimeters of rectangles and other polygons, and solve problems where one side length is unknown.
For a rectangle, children notice that opposite sides are the same length, so the perimeter is twice the length plus twice the width. In harder problems, they work backward: if a rectangle has a perimeter of 30 feet and a width of 5 feet, then half of the perimeter, 15, is one width plus one length, so the length is 10 feet.
Why it matters
Perimeter is a practical measurement: how much fence goes around a garden, how much ribbon goes around a card, or how far it is to walk around a field. It gives children a reason to add several lengths and to think about the properties of shapes.
It also helps children tell area and perimeter apart, which is important in later grades. Two rectangles can have the same area but different perimeters, or the same perimeter but different areas. Exploring this builds careful thinking about what is being measured, and working backward from a perimeter is good early practice for solving equations.
Common mistakes
- Confusing perimeter with area, and multiplying the side lengths. Tracing a finger around the edge of the shape while saying "perimeter is the path around" helps.
- Adding only the two side lengths that are labeled and forgetting the sides that are not. Labeling all four sides of a rectangle before adding prevents this.
- Giving perimeter in square units. Perimeter is a length, so it is measured in inches, feet or centimeters, not square units.
- Getting stuck when the perimeter is given and a side is missing. Drawing the shape and filling in what is known usually shows the way.
How to help at home
- Measure the perimeter of a table, a book or a rug with a tape measure, side by side.
- Walk the perimeter of a room or a playground, counting steps, and compare different spaces.
- Build rectangles from a piece of string of fixed length and see how many shapes have the same perimeter.
- Use a garden or fence question: "We want to put a border around this flower bed. How long does it need to be?"
- Trace a finger around picture frames, cereal boxes and placemats, then measure each side and add them up. Ask which side lengths you only needed to measure once.
Worked examples
These are real questions from the Tutorsaurus perimeter of rectangles practice, with the answers worked out.
Example 1
What is the perimeter of a 5 in by 6 in rectangle?
Answer: 22 in. Add all four sides: 5 + 6 + 5 + 6 = 22 in.
Example 2
What is the perimeter of a 9 in by 9 in rectangle?
Answer: 36 in. Add all four sides: 9 + 9 + 9 + 9 = 36 in.
Example 3
What is the perimeter of a 6 in by 3 in rectangle?
Answer: 18 in. Add all four sides: 6 + 3 + 6 + 3 = 18 in.