Area and perimeter: learn and practice

Who this lesson is for

This area and perimeter lesson is for grades 4–5. Students find both measures for a rectangle from the length and the width. The practice link opens rectangle area at grade 4. Triangle area is a later catalog skill and is not this page. The grade 4 and grade 5 hubs link here.

Area covers, perimeter walks the edge

Area is the number of square units that cover a rectangle. A rectangle that is 5 units long and 4 units wide holds 5 × 4 = 20 squares. Perimeter is the distance around the outside. The same rectangle has two lengths and two widths, so the walk is 5 + 4 + 5 + 4 = 18. Covering and walking are different questions. A larger area does not tell you the perimeter, and a longer walk does not tell you the area.

Opposite sides match

A rectangle has two pairs of equal sides. If you know one length and one width, you know all four sides. The perimeter is 2 × (length + width). The area is length × width, with no doubling. Mixing those two formulas is the usual error: doubling a product gives neither the area nor the perimeter.

Worked example 1: a 5 by 4 rectangle

A rectangle is 5 units by 4 units. The area is 5 × 4 = 20 square units. You can see it as 5 rows of 4 squares, or 4 rows of 5 squares. The perimeter uses every outer edge: 5 + 4 + 5 + 4 = 18 units. The 20 and the 18 answer different questions. Labeling 20 as the perimeter, or 18 as the area, swaps the two ideas.

Worked example 2: perimeter of a 6 by 3 rectangle

Find the perimeter of a rectangle that is 6 by 3. Opposite sides match, so the sides are 6, 3, 6, and 3. Add them: 6 + 3 + 6 + 3 = 18. The short form is 2 × (6 + 3) = 2 × 9 = 18. The area of this same rectangle would be 6 × 3 = 18 as well, which is a coincidence of these particular numbers. The units still differ: 18 units of length around the edge, against 18 squares of area.

Worked example 3: a square with side 4

A square is a rectangle whose sides are equal. Side 4 means length 4 and width 4. The area is 4 × 4 = 16 square units. The perimeter is 4 + 4 + 4 + 4 = 16 units, or 4 × 4 only because there are four equal sides, which happens to use the same arithmetic as the area. Change the side to 5 and the area becomes 25 while the perimeter becomes 20. The match at side 4 does not mean the two measures are the same idea.

Checks before you leave the problem

If the question says cover, or area, multiply the two different sides once. If it says around, or perimeter, add all four sides. Write the unit: squares for area, and a length for perimeter. Then practice rectangle area on the board.

Common questions about area and perimeter

Can the area and the perimeter be the same number?

Sometimes, as with a 6 by 3 rectangle or a square of side 4. The number matching does not make the measures the same. One counts squares. The other adds lengths.

Do I double the area to get the perimeter?

No. Area is length × width. Perimeter is 2 × (length + width). Doubling the area is a different calculation and does not walk the edge.

What about a triangle?

Triangle area uses half of base times height, and that skill is separate in the catalog. This page stays with rectangles, including squares.