Surface Area of a Rectangle Formula

Introduction to Surface Area of a Rectangle

A rectangle is a four-sided polygon with opposite sides that are equal in length and four right angles. It is a special case of a parallelogram where all angles are right angles. The rectangle has several important properties, and its formulas are used to calculate its various attributes.

Perimeter of a Rectangle:

Definition of Perimeter of a Rectangle: The perimeter of a rectangle is the total distance around its boundary.

Equation of Perimeter of a Rectangle: Perimeter = 2(length + width)

Where,

length is the length of the longer side (also known as the longer base) and

width is the length of the shorter side (also known as the shorter base)

Surface Area of a Rectangle:

Definition of Area of a Rectangle: The area of a rectangle is the measure of the surface enclosed by its four sides.

Equation of Area of a Rectangle: Area = length * width

Where,

length is the length of the longer side and

width is the length of the shorter side.

Diagonal of a Rectangle:

Definition of Diagonal of a Rectangle: The diagonal of a rectangle is the line segment connecting two opposite corners of the rectangle.

Equation of Diagonal of a Rectangle:

Diagonal = ⎷ {(length)2 + (width)2}

Where,

length is the length of the longer side and

width is the length of the shorter side.

Important Properties of Rectangle Formulas

Perimeter of a rectangle:

• The perimeter of a rectangle is found by adding up the lengths of all its sides.
• Since opposite sides of a rectangle are equal in length, the perimeter formula is simply twice the sum of the length and width. T
• This formula is useful in determining the amount of fencing needed to enclose a rectangular area or calculating the distance around a rectangular path.

Area of a rectangle:

• The area of a rectangle represents the measure of the surface enclosed by its sides.
• It is calculated by multiplying the length and width of the rectangle.
• This formula is employed in determining the amount of material required to cover a rectangular surface or finding the area of a rectangular field or room.

Diagonal of a rectangle:

• The diagonal of a rectangle is the line segment that connects two opposite corners of the rectangle.
• It divides the rectangle into two congruent right triangles.

Solved Examples on Rectangle formula:

Example 1. Perimeter of a Rectangle

Given: Length = 6 cm, Width = 4 cm

To find: Perimeter of the rectangle

Using the formula: Perimeter = 2(length + width)

Perimeter = 2(6 cm + 4 cm)

= 2 * 10 cm

= 20 cm

Therefore, the perimeter of the rectangle is 20 cm.

Example 2. Area of a Rectangle

Given: Length = 8 m, Width = 5 m

To find: Area of the rectangle

Using the formula: Area = length * width

Area = 8 m * 5 m

Area = 40 m2

Therefore, the area of the rectangle is 40 square meters.

Frequently asked questions on Rectangle formula:

1: What is the difference between length and width in a rectangle?

Answer: In a rectangle, the length refers to the longer side or base, while the width refers to the shorter side or base. The length is usually greater than the width.

2: How you find the area of a rectangle?

Answer: To find the area of a rectangle, you multiply the length of the rectangle by its width. The formula for the area of a rectangle is:

Area = Length × Width

For example, if you have a rectangle with a length of 6 units and a width of 4 units, the area would be:

Area = 6 units × 4 units = 24 square units

So the area of the rectangle in this case is 24 square units.

3: Can a rectangle have sides with fractional or decimal values?

Answer: Yes, the sides of a rectangle can have fractional or decimal values, depending on the specific measurements involved. The formulas for perimeter, area, and diagonal can handle such values in their calculations.

4: Can a rectangle have sides with negative values?

Answer: In mathematics, a rectangle’s sides are typically considered to have positive values, representing lengths. Negative lengths are not conventionally used when dealing with geometric shapes.

5: What if the dimensions of a rectangle are given in different units?

Answer: If the dimensions of a rectangle are given in different units, it is important to convert them to the same unit before using the formulas. Consistency in units is necessary for accurate calculations.

6: Can the perimeter or area of a rectangle be zero?

Answer: No, the perimeter and area of a rectangle cannot be zero. By definition, a rectangle has non-zero sides, and the formulas yield positive values for the perimeter and area.

7: Can the diagonal of a rectangle be greater than its perimeter?

Answer: No, the diagonal of a rectangle cannot be greater than its perimeter. The perimeter represents the total length of the sides, while the diagonal is a line segment connecting two opposite corners. In a rectangle, the diagonal is always shorter than the perimeter.

8: How to Find the Area of a Rectangle Using Diagonal?

Answer: The area of a rectangle can be calculated if the diagonal and one of its sides is given. We can find the value of the missing side using the Pythagoras theorem and then find the area. For example, let us find the area of a rectangle in which the diagonal is 10 units and its length is 8 units using the following steps.

Step 1: In this case, we can find the width using the formula, Width = ⎷[(Diagonal)2 – (Length)2]

Step 2: After substituting the given values, we get, width = ⎷[(10)2 – (8)2] = ⎷36 = 6 units

Step 3: Now, we know that the length = 8 units, width = 6 cm. So, the area of the rectangle = l × w. In this case, Area = 8 × 6 = 48 unit2