Area Of A Rectangle

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According to simple geometry, we can define the area of rectangle as the space occupied by a rectangle in a two-dimensional plane. Recall that a rectangle is one of the many types of quadrilateral. In other words that better describes it, a rectangle is a 2 dimensional shape made up of four vertices and four sides. Take good note that each of the four angles in a rectangle are equal to 90 degrees (that is to say right angles). Parallel to each other, the opposite sides of a rectangle are equal. Although both the rectangle and the parallelogram have their opposite sides parallel and equal to each other, the angles of a parallelogram are not right angles (that is not equal to 90 degrees).

What Is The Area Of A Rectangle

The Area of rectangle can be defined as the total region within which a rectangle is bounded fully by its four sides. Now, this is How To Find The Area Of A Rectangle.

Thus, the area of any given rectangle is totally dependent on its four sides. Basically, the formula for calculating the Area of Rectangle is equal to the product its length and breadth. However, this should not be confused with the perimeter of a rectangle which measures the distance round the shape. When we bring the perimeter of a rectangle into view then, we are talking about the sum of all its four sides. Hence, it is worthy to reiterate that the enclosed region within the perimeter of the rectangle is referred to as its area. Bringing the square into the limelight, all of its four sides are equal. Therefore, the area of a square can be calculated as the square of its side-length.

How To Find The Area Of A Rectangle = Length x Breadth
A = lb

Formula For Area of A Rectangle

To find the area of a rectangle formula, the width (breadth) and the length are the determinant factors. Thus, we can deduce that multiplying the length of a rectangle by its breadth (also called width) gives us the area of a rectangle in units.

Surface Area Of A Rectangle

Specific for three-dimensional figures and shapes, the total surface areas as well as the Lateral surface areas can be calculated. And since the rectangle is a tow-dimensional figure, it is not practical calculating the lateral and total surface areas. Hence, the perimeter and the area of a rectangle is given by:

Area Of A Rectangle Calculator

The formula for the Area of a Rectangle
Area of a Rectangle A = l × b

From the above explanations so far, you can agree that once the length and breadth of a rectangle are known, one can easily calculate the are of a rectangle. Simply multiply length and width in order to obtain a rectangle’s area in a square-unit dimension. If it were to be a square then, the area of the square can be calculated as the Side². The major characteristic that differentiates a rectangle from a square is that all the four sides of a square (length and width) are equal while those of a rectangle are not.

How Do You Find The Area Of A Rectangle

How to Calculate Area of a Rectangle

This is how to get the area of a rectangle. Follow the steps below to calculate the area of a Rectangle

First Step: Take a good note of the width and length dimensions of the rectangle from the information you are given.

Second Step: Multiply value of length of the rectangle with the width of the rectangle.

Third Step: Present your answer in square units.

Area of Rectangle Using Diagonal

Traditionally, you can calculate the diagonal of any rectangle using the formula given below:

(Diagonal)² = (Length)² + (Width)²

From this,

(Length)² = (Diagonal)² – (Width)²

Length = √Diagonal² – Width²

Or

(Width)² = (Diagonal)² – (Length)²

Width = √Diagonal² – Length²

Now, the area of rectangle = Length × Width

Area = Length × √Diagonal² – Length²

Or

Area = √Diagonal² x Width² × Width

What Is The Formula For The Area Of A Rectangle

Below are some special formulas related to the rectangle area.

How to find the area with diagonal of rectangle and width
Formula: Area = √Diagonal² – Width²

Find a missing side length when the area is known
Formula: Length = Area ÷ Width

How To Find The Area Of A Rectangle With Variables

A rectangle is divided into two equivalent right-angled triangles by its diagonal. Therefore, it follows that the sum of the respective areas of these two triangles will definitely amount to the area of the rectangle.

Suppose, ABCD is a rectangle.

Area of Rectangle using Length and Breadth

Now, let diagonal AC divide the rectangle into two right triangles, i.e. ∆ABC and ∆ADC.

We know that ∆ABC and ∆ADC are congruent triangles.

Area of ∆ABC = ½ x base x height = ½ x AB x BC = ½ x b x l

Area of ∆ADC = ½ x base x height = ½ x CD x AD = ½ x b x l

Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC

Area (ABCD) = 2(½ x b x l)

Area (ABCD) = l x b

Thus, the area of the rectangle = Length x Breadth

Area Of Rectangle Solved Examples

Example 1: Find the area of a rectangular shape with length 250cm and breadth 200 cm, respectively.

How To Find The Area Of A Rectangle:

Length of the Rectangle = 250 cm = 2.5 m

Breadth of the Rectangle = 200 cm = 2 m

Area of the Rectangle = length x breadth = 2.5 m x 2 m = 5 square-metres

Example 2: The length and width of a rectangular chalkboard are 25 m and 5 m, respectively. Work out the cost of shading the chalkboard if the rate of shading is $4 per square meter.

How To Find The Area Of A Rectangle:

Length of the chalkboard = 25 m

The breadth of the chalkboard = 5 m

Area of the chalkboard = length x breadth = 25 m x 5 m = 125 sq. m

For 1 square meter of shading, the cost is $4

Thus, for 125 square meters, the cost of shading the chalkboard will be calculated as = $4 x 125 = $500

Example 3: A cement walkway whose length is 300m and width 90m needs to be decorated all over coloured rectangular tiles. The dimension of each tile is 1.5 m wide and 2 m long. Find the total number of tiles that would be required to fully decorate the cement floor.

How To Find The Area Of A Rectangle:

Length of the floor = 300 m

The Width of the floor = 90 m

Area of the floor = length x Width = 300 m x 90 m = 27,000 square meters

Length of a tile = 2 m

The width of a tile = 1.5 m

Area of a tile = length x breadth = 2 m x 1.5 m = 3 square meters

Therefore, number of tiles needed = area of cement floor/area of a tile = 27,000/3 = 9,000 tiles

Example 4: A rectangle has a length of 40 cm and a width of 2 cm. Find the area of the rectangle presenting your answer in square meters.

How To Find The Area Of A Rectangle:

We were given the following information,

Length = 40 cm

Width = 2 cm

Area of a rectangle = Length × Width

40 × 2 = 80

So the area of rectangle = 80 cm²

Example 5: The length of a rectangular screen is 30 cm while the area it covers is calculated to be 360 square cm. Determine the width of this rectangular screen showing all workings.

How To Find The Area Of A Rectangle:

Area of the rectangular screen = 360 sq. cm.

Length of the rectangular screen = 30 cm

Area of a rectangle = length x width

So, width = area/length

Thus, width of the rectangular screen = 360/30 = 12 cm

What is the unit of area?

The unit of area of any given shape is a square unit. For example square meters or m².

What is the area of rectangle?
The area of the rectangle can be defined as the total space enclosed by the 4 sides of a rectangle.

What is the formula for area of rectangle

The formula for calculating the area of a given rectangle is written below:
Area = Length x Breadth

Why is the area of rectangle LB?

The area of any rectangle is LB (that is length x Breadth) it is the practical way of calculating the square units of the rectangle accurately. Thus, when you multiply the total squares in the length of a rectangle and the total squares in the width of a rectangle, you will get the total squares in rectangle which is its area.

What is the perimeter of rectangle?

The perimeter of a rectangle calculated by adding up values of the four side of a rectangle. Hence, it is equal to the sum of the four sides of a rectangle. So we can say that the Perimeter of a Rectangle = 2 x (Length + Breadth)

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