Session 4: Area of Rectangle – Formula, Definition, Interactive and Examples

Early human beings built their huts and erected tents with an intuitive notion of geometry. It is often claimed that geometry was the gift of the Nile. Early civilisations had a practical approach to geometry. They knew how to calculate the area of a triangle or a rectangle and had knowledge of the basic units of measurement. In these civilisations, two-dimensional geometrical forms like triangles, squares, circles, hexagons and octagons have been explored in architecture. Whether it’s the Great Bath of Mohenjodaro or the Great Wall of China of the Chinese civilisation, looking at the perimeter and area can help us understand the vastness of the project and help us analyse and give insight into the civilisation that created it.

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What is Area?

The area is the amount of surface enclosed by a closed two-dimensional figure. It is measured by the number of unit squares it takes to cover a two-dimensional shape. For example, if you count the small squares, you will find there are 15 of them. Therefore, the area is 3⋅5 or 15 unit².

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Area of Rectangle

A rectangle is a plane figure whose opposite sides (facing each other) are of equal lengths. So, we have two equal lengths (bases) and two equal heights (breadths). The area of a rectangle is the number of unit squares it takes to cover a rectangle.

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Formula for Area of Rectangle

Consider a rectangle shown below. Let b and ℎ denote its base and height respectively. The area of a rectangle is base b times height ℎ.

It follows from this formula that

base= \(\frac{Are{{a}_{rectangle}}}{height}\)
height= \(\frac{Are{{a}_{rectangle}}}{base}\)

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Area of Rectangle – Examples

Example 1

Find the area of a rectangle whose length is 16 units and breadth is 7 units.

We know, area of a rectangle = length ×breadth

 =16×7
=112 units²

Example 2

Find the length of the rectangle whose breadth is 25 mm and area is 900 mm².

We know,

Area of a rectangle = length × breadth

∴ Length of the rectangle= \(\frac{Are{{a}_{rectangle}}}{breadth}\)

=\(\frac{900}{25}\)
=36 mm

Example 3

The length of a rectangular park is twice its breadth. If the perimeter of the park is 72 m, find its area.

Let the breadth of the park be x meters. Then, its length =2x meters.

Then, its length =2x meters.

∴ Perimeter of the rectangular park =2 (length + breadth)                                                             

Given, perimeter of the park = 72 m. 

∴ breadth of the park = 12 m.

Hence, length of the park =2x=2×12=24 m.

∴ Area of the rectangular park = length × breadth                                                    

Example 4

How many envelopes can be made out of a sheet of paper 2 m by 1 m supposing each envelope requires a piece of paper of size 40 cm by 25 cm?

We know,

Area of the sheet =2 m×1 m                             

Area of paper required for one envelope=40 cm×25 cm

                                                                     =(40×25) cm2

Number of envelopes =\(\frac{Area of the sheet}{Area of paper required for one envelope}\)                                    

Example 5

If the area of a rectangle is 48 cm² and the length and width are whole numbers, find the maximum possible perimeter of the rectangle.

Let the length and width of the rectangle be l and w, respectively.

Area of rectangle =l×w.

∴l×w=48 cm².

The possible pairs are (48,1),(24,2),(16,3),(12,4) and (8,6).

∴ The maximum possible perimeter of the rectangle, P=2(l+w)=2(48+1)=98 cm

Remember this!

• The area is the amount of surface enclosed by a closed two-dimensional figure.
• The formula for the area of a rectangle is: 
  Area_rectangle=base×height
• Using the formula for the area of a rectangle, we can find the base and height of the rectangle: 
  base= \(\frac{Are{{a}_{rectangle}}}{height}\)
  height=\(\frac{Are{{a}_{rectangle}}}{base}\)