Rectangle Area and Perimeter: Formulas, Calculator & Examples

📐 Results:

\[A = 84 \text{ cm}^2\]

\[P = 46 \text{ m}\]

\(A = l \times w\)
\(A = 6 \times 4\)
\(A = 24 \text{ m}^2\)

\(P = 2(l + w)\)
\(P = 2(6 + 4)\)
\(P = 2(10)\)
\(P = 20 \text{ m}\)

The formula for the area of a rectangle is: Area = length × width or \(A = l \times w\). Multiply the length by the width to find the area. The result is expressed in square units (e.g., cm², m², ft²). For example, if a rectangle has length 10 cm and width 6 cm, the area is \(10 \times 6 = 60\) cm². This formula works because area measures how many unit squares fit inside the rectangle.

The formula for the perimeter of a rectangle is: Perimeter = 2(length + width) or \(P = 2(l + w)\). You can also write it as \(P = 2l + 2w\). Add the length and width, then multiply by 2, or add all four sides together. The result is expressed in linear units (e.g., cm, m, ft). For example, if length = 10 cm and width = 6 cm, perimeter = \(2(10 + 6) = 2(16) = 32\) cm. This represents the total distance around the rectangle.

To calculate the area of a rectangle: (1) Identify the length and width – measure or find the dimensions, making sure they're in the same units. (2) Multiply length × width – use the formula \(A = l \times w\). (3) Express the answer in square units – if measurements are in cm, area is in cm²; if in meters, area is in m². Example: Rectangle with length 8 cm and width 5 cm has area \(8 \times 5 = 40\) cm². Always include square units in your answer!

Area measures the space inside the rectangle (how much surface it covers) using \(A = l \times w\), expressed in square units. Perimeter measures the distance around the rectangle (the total length of all sides) using \(P = 2(l + w)\), expressed in linear units. Think of it this way: area is like carpeting a floor (inside), while perimeter is like putting a fence around a garden (border). Area uses multiplication; perimeter uses addition. They measure completely different things and have different units!

Yes! Two rectangles can have the same perimeter but very different areas. Example: Rectangle A is 10 cm × 2 cm: perimeter = \(2(10+2) = 24\) cm, area = \(10 \times 2 = 20\) cm². Rectangle B is 6 cm × 6 cm: perimeter = \(2(6+6) = 24\) cm, area = \(6 \times 6 = 36\) cm². Both have 24 cm perimeter, but B has much more area! In fact, for a given perimeter, a square (where length = width) always has the maximum area. This is an important concept in optimization problems.

Yes, absolutely! Length and width must be in the same units before you calculate area or perimeter. If length is in meters and width is in centimeters, you must convert one to match the other first. For example, if length = 2 m and width = 50 cm, convert to: length = 200 cm and width = 50 cm (both in cm), OR length = 2 m and width = 0.5 m (both in m). Then you can multiply or add correctly. Mixed units will give wrong answers and wrong unit labels.

Area is always measured in square units because you're measuring two-dimensional space (length × width = area). Common units: mm² (square millimeters), cm² (square centimeters), m² (square meters), km² (square kilometers), in² (square inches), ft² (square feet), yd² (square yards), mi² (square miles). Perimeter is measured in linear units because you're measuring one-dimensional distance around the shape. Common units: mm, cm, m, km, in, ft, yd, mi. If your measurements are in cm, area will be cm² and perimeter will be cm.

Yes! A square is a special type of rectangle where all four sides are equal (length = width). Since a rectangle is defined as a quadrilateral with four right angles, and a square has four right angles, a square meets the definition of a rectangle. All the formulas work: for a square with side \(s\), area = \(s \times s = s^2\) and perimeter = \(2(s + s) = 4s\). However, not all rectangles are squares – only those where length equals width. Think of it as: all squares are rectangles, but not all rectangles are squares.