How to Calculate Area of a Rectangle

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The area of a rectangle is a fundamental concept in mathematics and is commonly used in various fields such as geometry, architecture, and engineering. It refers to the amount of space enclosed by the rectangular shape and can be calculated by using a simple formula. Understanding how to calculate the area of a rectangle is essential for solving mathematical problems and real-life applications that involve measuring and analyzing rectangular shapes. In this guide, we will explore the step-by-step process of calculating the area of a rectangle, including the necessary formula, variables, and examples to enhance comprehension. Whether you are a student seeking to improve your math skills or an individual looking to better understand the concepts behind rectangle measurements, this guide will provide you with the knowledge and tools to calculate the area of a rectangle accurately.

A rectangle is a quadrilateral with 2 equal lengths and 2 equal widths creating 4 right angles. To calculate the area of a rectangle, you simply multiply the length by the width. If you want to know how to find the area of a rectangle, follow these steps.

Table of Contents

Steps

Overview of the Rectangle

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Learn about rectangles. A rectangle is a quadrilateral, meaning it has 4 sides. Its lengths are equal and so are its widths. If one length has a measure of 10, the other length is also 10.

• Also, every square is a rectangle but not all rectangles are squares. So when we calculate the area of a square, we do the same with the rectangle.

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Formula for calculating the area of a rectangle. The calculation of the area of a rectangle is very simple, S = D * R (the equivalent in the figure is L * W). This means that the area is equal to the length times the width.

Find the area of a rectangle

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Find the length of the rectangle. In most problems, the question will give you the length, but if not, use a ruler to measure.

• Note that 2 slashes on the lengths mean they are equal.

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Find the width of the rectangle. Use the same method to find.

• Note that slashes on widths mean they are equal.

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Write the length and width measurements side by side. In this example, the length is 5 cm and the width is 4 cm.

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Multiply the length by the width. The length is 5 cm and the width is 4 cm, combine them into the formula S =D * R to calculate the area.

• A = 4 cm * 5 cm
• A = 20 cm ²

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Record your answer in squared units. Your answer is 20 cm ² , which means “twenty square centimeters”.

• You can write the final answer in two ways: 20 square centimeters or 20 centimeters ² .

Find the area if only the length of one side and the diagonal is known

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Understand Pythagorean Theorem. The Pythagorean Theorem is a formula for calculating the length of the third side when the lengths of the 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 make up the right angle.

• Since a rectangle has 4 right angles, the diagonal crossing it will create a right triangle, so we can apply the Pythagorean theorem.
• The theorem is: a ² + b ² = c ² , where a and b are the 2 sides of the right angle and c is the hypotenuse – also the longest side.

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Use the Pythagorean theorem to calculate the remaining side of the triangle. Let’s say you have a triangle with a side 6 cm long and a diagonal 10 cm. Let 6 cm be the length of one side, b the other side, and 10 cm the hypotenuse. Substitute the data into the Pythagorean theorem and solve the problem as follows:

• Example: 6 ² + b ² = 10 ²
• 36 + b ² = 100
• b ² = 100 – 36
• b ² = 64
• Square root of (b) = square root of (64)
• b = 8
  • The remaining length of the triangle, which is also the length of the rectangle, is 8 cm.

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Multiply the length by the width. You just used the Pythagorean theorem to find the length and width, now you just need to multiply them together.

• Example: 6 cm * 8 cm = 48 cm ²

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Record your answer in squared units. Your final answer is 48 cm ² , or 48 square centimeters.

Advice

• Every square is a rectangle but not all rectangles are squares.
• If you calculate the area, the answer is always squared

A rectangle is a quadrilateral with 2 equal lengths and 2 equal widths creating 4 right angles. To calculate the area of a rectangle, you simply multiply the length by the width. If you want to know how to find the area of a rectangle, follow these steps.

In conclusion, calculating the area of a rectangle is a simple yet important concept in mathematics. By multiplying the length and width of the rectangle, we can easily determine the amount of space it occupies. This calculation is not only useful in solving mathematical problems but also in real-life applications such as construction, interior design, and land surveying. Understanding how to calculate the area of a rectangle is fundamental as it forms the basis for more complex geometric calculations. By mastering this simple formula, individuals can develop a solid foundation for further mathematical learning and problem-solving skills.

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