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Area vs Perimeter
Counting Squares and Measuring Around
Related Worksheets
Area and perimeter are two different ways to describe a flat shape. Area tells how much space is covered inside the shape, while perimeter tells the distance around its outside edge. These ideas matter when you plan flooring, paint a wall, build a fence, or compare the size of figures on a grid. Counting squares and measuring around are simple visual methods that help make the difference clear.
On a square grid, area is found by counting the unit squares inside the shape. Perimeter is found by counting the unit lengths along the outside boundary, including every exposed side of each edge square. Rectilinear shapes are made from horizontal and vertical sides, so they are especially useful for learning these ideas. Two shapes can have the same area but different perimeters, or the same perimeter but different areas.
Key Facts
- Area measures the space inside a shape and is written in square units.
- Perimeter measures the total distance around a shape and is written in linear units.
- Rectangle area: A = l × w
- Rectangle perimeter: P = 2l + 2w
- On a unit grid, area equals the number of full unit squares inside the shape.
- On a unit grid, perimeter equals the number of unit-length edges around the outside boundary.
Vocabulary
- Area
- Area is the amount of flat space inside a two-dimensional shape.
- Perimeter
- Perimeter is the total distance around the outside edge of a two-dimensional shape.
- Unit square
- A unit square is a square with side lengths of 1 unit and an area of 1 square unit.
- Rectilinear shape
- A rectilinear shape is a polygon made only from horizontal and vertical line segments.
- Boundary
- The boundary is the outer edge or outline of a shape.
Common Mistakes to Avoid
- Counting inside squares for perimeter is wrong because perimeter only measures the outside boundary, not the filled space.
- Writing area in units instead of square units is wrong because area counts two-dimensional space, such as square centimeters or square meters.
- Counting shared edges inside a shape as part of the perimeter is wrong because edges between two filled squares are not on the outside boundary.
- Assuming a bigger area always means a bigger perimeter is wrong because the shape's arrangement affects the length around it.
Practice Questions
- 1 A rectangle is 8 units long and 5 units wide. Find its area and perimeter.
- 2 An L-shaped figure is made from 10 unit squares. The outside boundary has 18 unit edges. What are its area and perimeter?
- 3 Two shapes are each made from 12 unit squares. One is a 3 by 4 rectangle, and the other is a long 1 by 12 rectangle. Explain why they have the same area but different perimeters.