how to find width of a rectangle

In geometry, a rea of rectangle is the region covered by the rectangle in a ii-dimensional airplane. A rectangle is a type of quadrilateral, a 2d shape that has iv sides and four vertices. All the 4 angles of the rectangle are right angles or equal to 90 degrees. The reverse sides of the rectangle are equal and parallel to each other. To be noted, a parallelogram also has its opposite sides equal and parallel to each other but the angles are not equal to 90 degrees.

What is the Area of Rectangle?

Definition: Area of rectangle is the region occupied by a rectangle inside its iv sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle , it is equal to the sum of all its four sides. Hence, we tin say, the region enclosed by the perimeter of the rectangle is its area. Just in the example of a square, since all the sides are equal, therefore, the surface area of the foursquare will be equal to the foursquare of side-length.

Expanse of rectangle = Length x Latitude

A = lb

Area of Rectangle Formula

The formula to find the area of rectangle depends on its length and width. The area of a rectangle is calculated in units past multiplying the width (or breadth) past the Length of a rectangle. Lateral and total surface areas can exist calculated just for three-dimensional figures. Nosotros cannot summate for the rectangle since it is a two-dimensional figure. Thus, the perimeter and the area of a rectangle is given by:

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

The expanse of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle'south area will obtain in a square-unit dimension. In the case of a square, the expanse will get side². The main deviation between square and rectangle is that the length and breadth are equal for square.

How to Calculate the Area of a Rectangle

Follow the steps beneath to find the area:

Pace 1 :  Note the dimensions of length and width from the given data

Step 2 : Multiply length and width values

Pace 3: Write the reply in square units

Area of Rectangle Using Diagonal

We know that the diagonal of a rectangle is calculated using the formula:

(Diagonal) ^two = (Length)²  + (Width)^two

From this,

(Length)ⁱⁱ  = (Diagonal)²  – (Width)²

Length =

\(\brainstorm{array}{fifty}\sqrt{Diagonal^ii – Width^ii}\end{assortment} \)

Or

(Width)²  = (Diagonal)^two  – (Length)²

Width =

\(\begin{array}{50}\sqrt{Diagonal^ii – Length^2}\terminate{assortment} \)

Now, the area of rectangle = Length × Width

Area = Length ×

\(\brainstorm{array}{50}\sqrt{Diagonal^2 – Length^ii}\stop{array} \)

Or

Expanse =

\(\begin{array}{50}\sqrt{Diagonal^two – Width^2}\cease{assortment} \)

× Width

Important Facts

Below are some special formulas related to the rectangle area.

1. How to find the expanse with diagonal of rectangle and width

          Formula: Area =

\(\begin{array}{l}Width\ \sqrt{(Diagonal^2 – Width^2)}\cease{array} \)

2. Notice a missing side length when the area is known

           Formula: Length = Expanse/Width

Why Area of the rectangle is length x latitude?

The diagonals of the rectangle split information technology into two equivalent right-angled triangles. Therefore, the expanse of the rectangle will be equal to the sum of the area of these two triangles.

Suppose, ABCD is a rectangle.

Now, let diagonal Air-conditioning carve up the rectangle into two correct triangles, i.e. ∆ABC and ∆ADC.

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

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

Area of ∆ADC = ½ ten base ten height = ½ 10 CD x Advertisement =  ½ 10 b x l

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

Area (ABCD) = 2(½ x b 10 l)

Area (ABCD) = l 10 b

Thus, the area of the rectangle = Length x Breadth

Related Articles

• Area Of A Triangle
• Expanse Of Square
• Expanse Of Quadrilateral
• Area Of Rhomb
• Area Of Trapezium
• Area Of Parallelogram
• Area of Circle

Expanse of rectangle Solved Examples

Example 1: Find the area of the rectangle whose length is fifteen cm and the width is iv cm.

Solution:

Given,

Length = xv cm

Width = four cm

Area of a rectangle = Length × Width

xv × 4  = sixty

So the surface area of rectangle = 60 cm^two

Example 2: Find the area of a rectangular blackboard whose length and latitude are 120 cm and 100 cm, respectively.

Solution:

Length of the blackboard = 120 cm = 1.2 m

Latitude of the blackboard = 100 cm = 1 g

Area of the blackboard = area of a rectangle = length x breadth = 1.two k x 1 m = i.2 square-metres

Example 3: The length of a rectangular screen is 15 cm. Its surface area is 180 sq. cm. Find its width.

Solution:

Area of the screen = 180 sq. cm.

Length of the screen = 15 cm

Area of a rectangle = length ten width

So, width = expanse/length

Thus, width of the screen = 180/fifteen = 12 cm

Instance 4: The length and latitude of a rectangular wall are 75 m and 32 m, respectively. Detect the cost of painting the wall if the rate of painting is Rs 3 per sq. g.

Solution:

Length of the wall = 75 1000

The breadth of the wall = 32 m

Surface area of the wall = length x latitude = 75 m x 32 m = 2400 sq. m

For 1 sq. one thousand of painting costs Rs 3

Thus, for 2400 sq. thou, the price of painting the wall will be = 3 x 2400 = Rs 7200

Example 5: A floor whose length and width is 50 m and 40 m respectively needs to be covered by rectangular tiles. The dimension of each tile is i m x 2 k. Find the full number of tiles that would exist required to fully cover the floor.

Solution:

Length of the floor = 50 m

The breadth of the flooring = 40 m

Area of the floor = length ten breadth = fifty thou x twoscore grand = 2000 sq. m

Length of one tile = 2 1000

The breadth of ane tile = 1 m

Surface area of i tile = length x breadth = two m x ane m = ii sq. one thousand

No. of tiles required = area of floor/area of a tile = 2000/2 = m tiles

Frequently Asked Questions on Surface area of Rectangle

What is the formula for expanse of rectangle?

The formula for expanse of rectangle is:
Area = Length x Breadth

What is the perimeter of rectangle?

The perimeter of the rectangle is the sum of all its iv sides. Hence,
Perimeter (rectangle) = 2 (Length + Breadth)

What is the area of rectangle?

The area of the re ctangle is the region occupied past the sides of the rectangle.

Why is the area of rectangle LB?

The area of the rectangl e is LB because we calculate hither the square units of the recta ngle. After multiplying the total squares in the length and total squares in the width of the rectangle, will requite the total squares in rectangle.

What is the unit of area?

The unit of area of any shape is a square unit. For example, sq.m. or m^two.

Learn more than about the rectangle, perimeter of a rectangle, quadrilaterals etc. by visiting our page BYJU'South.

Source: https://byjus.com/maths/area-of-rectangle/

Posted by: hiersmorgilizeed.blogspot.com

Share this post