How to Calculate Area of a Rectangle

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

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.

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

Steps

Overview of the Rectangle

Find the area of a rectangle

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

Advice

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