What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance around it, calculated as 2 times the sum of its length and width (P = 2(l + w)).

Is a square a rectangle?

Yes, a square is a rectangle with four equal sides. Its perimeter is 4 times the side length (P = 4s), which is a special case of the rectangle formula.

How do I find a missing side from the perimeter?

If you know the perimeter and one side, divide the perimeter by 2, then subtract the known side. For a rectangle: missing side = (P ÷ 2) − known side. For a square: divide the perimeter by 4.

What is the difference between perimeter and area?

Perimeter is the distance around the outside (a linear measurement). Area is the space inside (a square measurement). Use perimeter for a fence, area for paint.

What units does perimeter use?

Perimeter uses linear units: inches, feet, meters, centimeters, etc. It is never squared. Always convert to the same unit before calculating.

Why is my measurement of a rectangle different from the formula?

Real-world measurements have errors from tape sag (1-3% under), non-square corners, and corner gaps. The formula assumes perfect right angles and straight sides. Measure twice and account for terrain.

Where is this taught in school?

Grade 3 (Common Core 3.MD.D.8) covers perimeter of polygons and missing sides. Grade 4 (4.MD.A.3) applies area and perimeter formulas. Grade 7 (7.G.B.4) extends to composite shapes.

Perimeter of a Rectangle: Formula, Examples, Missing Side

You Need the Perimeter of a Rectangle

To find the perimeter of a rectangle, add the length and width, then multiply by 2. This works for any rectangle, including squares. The formula is P = 2(l + w). For a square, since all four sides are equal, the formula simplifies to P = 4s, where s is the side length. The perimeter of a rectangle is a linear measurement, the total distance around the shape, not an area measurement, which is the space inside. This distinction is the most common mistake: confusing the boundary with the interior.

The Rectangle Perimeter Formula: Why 2(l + w)

A rectangle has two pairs of equal sides. Opposite sides are the same length. If you label the longer side as length (l) and the shorter side as width (w), then the perimeter is l + w + l + w. That is the same as 2l + 2w, which simplifies to 2(l + w). This formula works for any rectangle, regardless of its proportions. For example, a rectangle with a length of 8 inches and a width of 3 inches has a perimeter of 2(8 + 3) = 22 inches. Adding each side individually, 8 + 3 + 8 + 3, gives the same result.

Squares as a Special Case

A square is a rectangle with four equal sides. Because all sides are the same length, the perimeter formula for a rectangle, 2(l + w), becomes 2(s + s) = 4s, where s is the side length. If a square has a side length of 5 meters, its perimeter is 20 meters. Knowing this shortcut saves a step. However, you can still use the rectangle formula: 2(5 + 5) = 20 meters. The same principle applies to any rectangle where the length and width are equal, though that is only true for squares.

How to Find a Missing Side From the Perimeter

If you know the perimeter of a rectangle and one side, you can find the missing side. Rearrange the formula P = 2(l + w) to solve for the unknown side. For a rectangle with a known perimeter and known length, the width is (P ÷ 2) − l. For example, if the perimeter is 30 meters and the length is 10 meters, the width is (30 ÷ 2) − 10 = 5 meters. This works for rectangles and squares. For squares, divide the perimeter by 4 to get the side length. A square with a perimeter of 36 inches has a side length of 9 inches. Missing side problems appear on Grade 3 tests (Common Core 3.MD.D.8) and in real-world scenarios like figuring out how much fencing you need for a garden bed where you only know one dimension.

Mixed Units: Convert Before You Calculate

Before using the rectangle perimeter formula, ensure all side lengths are in the same unit. A rectangle with a length of 2 feet and a width of 6 inches gives a false result if you plug the numbers in directly: 2(2 + 6) = 16, but the unit is ambiguous. Convert 6 inches to 0.5 feet, then calculate 2(2 + 0.5) = 5 feet. Alternatively, convert 2 feet to 24 inches: 2(24 + 6) = 60 inches. Unit conversion is a prerequisite skill for Grade 4 (Common Core 4.MD.A.3). In real-world situations, tape sag and corner gaps add 1-3% to the actual measurement, so always measure twice and convert carefully.

Worked Examples: Perimeter and Reverse Problems

Find the Perimeter

A rectangle has a length of 12 cm and a width of 7 cm. Its perimeter is 2(12 + 7) = 38 cm. Adding each side: 12 + 7 + 12 + 7 = 38 cm. This is a direct application of the rectangle perimeter formula.

Find the Missing Side

The perimeter of a rectangle is 48 inches. The length is 15 inches. The width is (48 ÷ 2) − 15 = 9 inches. Check: 2(15 + 9) = 48 inches. This reverse problem is common in Grade 4 and Grade 7 (Common Core 3.MD.D.8, 4.MD.A.3, 7.G.B.4).

A Square: Perimeter Given

A square has a side of 9 feet. Its perimeter is 4 × 9 = 36 feet. For a square, the formula simplifies to 4s.

A Square: Missing Side

A square has a perimeter of 60 meters. Its side length is 60 ÷ 4 = 15 meters. This is the same as solving for a missing side in a rectangle where length equals width.

Mixed Units

A rectangle's length is 1.5 meters, and its width is 40 centimeters. Convert 40 cm to 0.4 m. Perimeter = 2(1.5 + 0.4) = 3.8 meters. Alternatively, convert 1.5 m to 150 cm: 2(150 + 40) = 380 cm. Both answers are equivalent.

For composite shapes, do not add the perimeters of each sub-shape; you will double-count shared interior edges. Instead, subtract the shared sides. For example, an L-shaped room made of two rectangles requires measuring all outer edges and not counting the wall where the rectangles meet. This is a Grade 7 skill (Common Core 7.G.B.4) and a common failure mode in real-world fence and trim measurements.