How to Calculate the Area of a Rectangle

A rectangle is a quadrilateral with two equal lengths and two equal widths, forming four right angles. To calculate the area of a rectangle, simply multiply its length by its width. If you're looking for a step-by-step guide on how to find the area of a rectangle, follow the steps below.

Understanding the Rectangle. A rectangle is a quadrilateral, meaning it has four sides. Its lengths are equal, and its widths are also equal. For example, if one length measures 10, the other length will also be 10.

• Additionally, every square is a rectangle, but not all rectangles are squares. Therefore, when calculating the area of a square, follow the same method used for rectangles.

Formula for Calculating the Area of a Rectangle. The calculation for the area of a rectangle is quite simple: A = L * W (equivalent to D * R in the diagram). This means the area is found by multiplying the length by the width.

Finding the Length of the Rectangle. In most problems, the length will be given to you, but if not, use a ruler to measure it.

• Note that the two diagonal lines across the lengths mean they are equal.

Finding the Width of the Rectangle. Use the same method to find the width.

• Note that the diagonal lines across the widths mean they are equal.

Record the Length and Width Measurements Together. In this example, the length is 5 cm and the width is 4 cm.

Multiply the Length by the Width. The length is 5 cm and the width is 4 cm. Plug these values into the formula A = L * W to calculate the area.

• A = 4 cm * 5 cm
• A = 20 cm²

Write the answer with the square unit. Your answer is 20 cm², meaning “twenty square centimeters.”

• You can write the final answer as either 20 square cm or 20 cm².

Understanding the Pythagorean Theorem. The Pythagorean Theorem is a formula for calculating the length of the third side when two sides of a right triangle are known. You can use this theorem to calculate the hypotenuse of a triangle, which is the longest side, or the sides that form the right angle.

• Since a rectangle has four right angles, the diagonal that cuts across the rectangle forms a right triangle, so the Pythagorean Theorem can be applied.
• The formula is: a² + b² = c², where a and b are the two sides of the right angle, and c is the hypotenuse — also the longest side.

Use the Pythagorean Theorem to find the missing side of the triangle. For example, suppose you have a triangle with one side of 6 cm and a diagonal of 10 cm. Let 6 cm be one side, b be the missing side, and 10 cm be the hypotenuse. Substitute the values into the Pythagorean formula and solve the equation as follows:

• Example: 6² + b² = 10²
• 36 + b² = 100
• b² = 100 - 36
• b² = 64
• The square root of b = the square root of 64
• b = 8
  • The remaining side of the triangle, which is also the length of the rectangle, is 8 cm.

Multiply the Length by the Width. After applying the Pythagorean Theorem to find the length and width, now simply multiply them together to get the area.

• Example: 6 cm * 8 cm = 48 cm²

Write the answer with the square unit. Your final answer is 48 cm², or 48 square cm.