Area of Rectangle Formula: Definition, Explanation, and Solved Examples
The area of a rectangle represents the quantity of unit squares that can be accommodated within its boundaries. In simpler terms, it quantifies the extent of space enclosed by a rectangle.
Anchal Singh12 Sept, 2023
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Area of Rectangle Formula is a four-sided polygon with all angles equal to 90 degrees, and its opposite sides are both equal and parallel. Rectangular shapes can be found all around us, each characterized by two dimensions: length and width. The longer side of a rectangle is referred to as its length, while the shorter side is called its width. In this chapter, we will explore the concept of rectangles, various formulas associated with them, different types of rectangles, and their properties.
What is the Area of a Rectangle Formula?
Definition of a Rectangle: A rectangle is a two-dimensional closed figure with four sides, four vertices, and four internal right angles. Its opposite sides are equal and parallel to each other.
Length and Width of a Rectangle:
The length of a rectangle denotes its longer side, while the width corresponds to the shorter side. It's worth noting that you can calculate the length of a rectangle if you know its area, perimeter, and width. Similarly, the width of a rectangle can be determined if you have information about its area, perimeter, and length.
Properties of a Rectangle
Rectangles possess several noteworthy properties, including: A rectangle is a quadrilateral with four sides. Its opposite sides are both equal and parallel. All interior angles of a rectangle measure 90 degrees. The sum of all interior angles in a rectangle is 360 degrees. The diagonals of a rectangle bisect each other. The lengths of the diagonals are equal. You can calculate the length of the diagonals using the Pythagoras theorem, where the diagonal with sides 'a' and 'b' is given by: diagonal = √(a^2 + b^2). Due to its parallel sides, a rectangle is also considered a parallelogram. While all rectangles are parallelograms, not all parallelograms are rectangles.Rectangle Formulas
Rectangles have fundamental formulas that help find missing or unknown values: Area of a rectangle formula: Area = Length × Width Perimeter of a rectangle formula: Perimeter = 2 × (Length + Width) Length of a rectangle formula: Length = Area ÷ Width or Length = (Perimeter ÷ 2) - Width Width of a rectangle formula: Width = Area ÷ Length or Width = (Perimeter ÷ 2) - LengthDiagonal of a Rectangle
The diagonal of a rectangle is a line segment connecting two non-adjacent vertices. In a rectangle, both diagonals have equal lengths, dividing the rectangle into two right-angled triangles.
Diagonal of Rectangle Formula
The formula for calculating the diagonal of a rectangle is derived using the Pythagoras theorem: Diagonal (d) = √(Length² + Width²)Download PDF Area Of Rectangle Formula
Area of a Rectangle Formula
The area of a rectangle represents the quantity of unit squares that can be accommodated within its boundaries. In simpler terms, it quantifies the extent of space enclosed by a rectangle. To illustrate, consider common rectangular objects like laptop screens, blackboards, or canvas paintings. We can employ the rectangle area formula to determine the amount of space these objects occupy. For instance, take a rectangle with dimensions of 4 inches in length and 3 inches in width. If we place unit squares within this rectangle, where each square has a side length of 1 inch, we can count the squares. In the diagram below, you'll notice that there are a total of 12 squares. As we've previously established, area is expressed in square units. Given that the unit of measurement for this rectangle is inches, we express the area in square inches. Therefore, the area of the rectangle is 12 square inches. Consequently, when we know the dimensions (length and width) of a rectangle, we can calculate its area.
Area of Rectangle Formula:
Area = Length × Width
Area of a Rectangle Formula Examples
Example 1: George possesses a rectangular photo frame measuring 6 inches in length and 3 inches in width. Can you assist George in determining its area? Solution:We can use the formula for calculating the area of a rectangle, which is Area = Length × Width. Therefore, the area of the rectangular frame is equal to 6 × 3 = 18 square inches. Hence, the area of the photo frame is 18 square inches. Example 2: Elsa intends to construct a rectangular fence for her garden. The perimeter of the fence is 30 feet, and the length of the fence is 10 feet. Can you aid Elsa in finding the breadth (width) of the fence? Solution: We are aware that the formula to calculate the perimeter of a rectangle is Perimeter = 2 × (Length + Width). Given the perimeter is 30 feet and the length is 10 feet, we can determine the width using the perimeter formula. Substituting the known values into the formula: Perimeter of a Rectangle = 2 × (10 + width), we have 30 = 2 × (10 + width). By solving further, we find that 10 + width = 15, and consequently, the width is 5 units. Hence, the width of the fence is 5 feet. Example 3: Determine whether the following statements are true or false: a.) The opposite sides of a rectangle are equal and parallel to each other. b.) The length of the diagonals can be obtained using the Pythagoras theorem. c.) All parallelograms are rectangles. Solution: a.) True, the opposite sides of a rectangle are indeed equal and parallel to each other. b.) True, the length of the diagonals can be determined using the Pythagoras theorem. c.) False, not all parallelograms are rectangles. Some parallelograms can also be squares or rhombuses.Area of a Rectangle Formula FAQs
What is a Rectangle?
A rectangle is a four-sided polygon with all angles equal to 90 degrees, and its opposite sides are both equal and parallel.
What is the formula for area of rectangle?
Area of Rectangle Formula:
Area = Length × Width
Give some examples of rectangle shaped object.
Books, Laptops, Windows etc.
What is the formula for calculating the diagonal of a rectangle?
The formula for calculating the diagonal of a rectangle.
Diagonal (d) = √(Length² + Width²)
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