Rectangle Formula

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Area of Rectangle Formula

The area of a rectangle is the region encompassed by the rectangle in a two-dimensional closed plane figure. In simple words, the area of a rectangle is the total space covered by the figure. On the other hand, the space within the bounds of the perimeter of the rectangle is also the area of a rectangle. Here, you will also get to know why the area of a rectangle is the product of its two sides and also the units of measurement.


What is a Rectangle?

A rectangle is a 2 dimensional geometric shape consisting of four sides, four angles and four vertices. Opposite sides of the rectangle are equivalent and parallel to each other in a rectangle. Remember that all the interior four angles of the rectangle are right angles. Pointing out, a parallelogram also has its opposite sides equal and parallel to each other but the angles do not make 90 degrees of measurement.


Important Rectangle Formulas

The formula of the area and perimeter of the rectangle is given below.

Given that ‘l’ represents the length and ‘b’ represents the breadth of the rectangle, then the


Element

Formula

Perimeter of rectangle formula

2(l + b) units

Length of the rectangle formula

P/2 - b units

Breadth of the rectangle

P/2 - l units

Area of rectangle formula

l × b sq. units

Length of the rectangle

A/b units

Breadth of the rectangle

A/l units

Diagonal of the rectangle

√(l²+b²) units


Derive and Calculate the Area of a Rectangle

To derive the area of a rectangle, we use the unit squares. Divide the rectangle MNOP into unit squares. The area of a rectangle MNOP is the total number of unit squares in it.

Now, finding the area of a rectangle

Rectangle MNOP in unit squares each with 1 sq. inch

Therefore, the total area of the rectangle MNOP is equal to 48 sq. inch.

Also, following the perspective, we discovered that the area of a rectangle is mandatorily the product of its two sides. Here, the length of MN is 6 inches and the breadth of NO is 8 inches. The area of MNOP is the product of 6 and 8, which is 48.

Instead, formulas to find the area of a rectangle is derived by dividing the figure into two equal-sized right triangles. For example, in the given rectangle MNOP, a diagonal from the vertex M is drawn to O.

The diagonal MO divides the rectangle into 2 equivalent right-angle triangles.

Therefore, the area of MNOP will be:

   ⇒ Area (MNOP) = Area (MNO) + Area (MPO)

   ⇒ Area (MNOP) = 2 × Area (MNO)

   ⇒ Area (MNO) = ½ × base × height

   ⇒ Area (MNOP) = 2 × (½ × b × h)

    ⇒ Area (MNOP) = b × h

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Application of Rectangle Formula

The early documentation script of Babylonian culture represents the use of geometric objects with lengths, width, angles, and areas for construction and astronomy. The skill and understanding of stone cutting in standard shapes such as squares, triangles and rectangles along with principles having reference to area and perimeter helped ancient Egyptians in constructing giant structures like pyramids. In modern times, these rectangle volume formula concepts are greatly helpful in object modelling, land surveying and others.


Examples of Rectangle

Some examples of rectangular figures are:

  • Parks and agricultural fields,

  • Painting Canvas

  • Tiles and walkway with rectangular tiles

  • Daily life objects such as a table, serving tray, glass, etc.

Solved Examples

Here, we will perform practical problems using step-by-step solutions in order to find the area of a rectangle as well as other measurements.


Example:

Calculate the area and the perimeter of the rectangle box that measures 15 cm in length and 8cm in breadth.


Solution:

Given:

Length = 15 cm,

Breadth = 8 cm

Now applying the area of rectangle formula i.e. = length × breadth

= (15 × 8) cm²

= 120 cm²

Using the formula for Perimeter of rectangle = 2 (length + breadth)

 = 2 (15 + 8) cm

= 2 × 23 cm 

= 46 cm


Example:

Evaluate the breadth of the Television set rectangular in shape whose area is 320 m2 and whose length is 40 m. Find its perimeter.


Solution:

We know that the breadth of the rectangular television set = Area/length

= 320m/40m

= 8 m

Thus, the perimeter of the rectangular television set = 2 (length + breadth)

= 2(40 + 8) m

 = 2 × 48 m

= 96 m


Fun Facts

  • In a rectangle, both the diagonals are equal in length.

  • We also have a rectangular figure that we call a cyclic rectangle. A circle that contains a rectangle with its entire vertex touching the circumference is a cyclic rectangle.

  • This concept of area calculation is also very useful in land surveying, map designing, modelling, and others.

FAQ (Frequently Asked Questions)

Q1. What Do We Understand by the Area of a Rectangle and Geometric Shapes?

Answer: When we discuss some plane figures, we think of their shape, edges, boundary and region. We typically compare the objects or a plane figure on the basis of their size, shape and area. We are well aware of the fact that we require some measure to compare these basic elements. Interestingly one such measure is its area. All the objects that lie within the bounds of a plane obtain some region of a flat surface. The measure of the surface circumscribed by a closed plane figure is what we call its area.

Q2. What are the Different Geometric Shapes?

Answer: There are various geometrical closed shapes/figures that exist namely— circle, square, rectangle, triangle, etc. Here, we have mainly focused on the understanding of the rectangle formula with some practical solved examples, its calculation, and units.

Q3. Why Length * Breadth is the Area of the Rectangle?

Answer: As you already know that the area of the rectangle is LB. This is because we calculate the area in the square units of the rectangle. After multiplying the total squares in the length and total squares in the breadth of the rectangle, will provide the total squares in the rectangle. Remember that the unit of area of the rectangle or any shape is a square unit. For example, sq.m. or m².