AREA

 The term “area” refers to the space inside the boundary or perimeter of a closed shape. 

The area is measured in square units such as square feet, square centimetres, square inches, etc.

The origin of the word is from ‘area’ in Latin, which translates to a vacant piece of level ground

Deriving area formulas

The “area” for any object  could be  explained as:

The amount of material (such as paper, fabric, tiles) required to cover the surface in a 2-dimensional plane.

Calculating the area

The easiest method to interpret the area of geometric shapes is using “unit squares”. A unit square is a square with each of its side length measuring 1 unit. Using this as a basis, the area of a polygon is the number of unit squares within a shape.

TRIANGLE:

Area =  1⁄2× base × height 

Area = 1⁄2 × b × h

EXAMPLE:

Find the area of a triangle with a base of 10 inches and a height of 5 inches.

Solution:

A = (1/2) × b × h

A = 1/2 × 10 × 5

A = 1/2 × 50

A = 25 in2

SQUARE:

Area = length × length or

Area = side ×side 

Example: 

Find the area of a square park whose side is 90 ft.

Solution:

Given: Side of the square park = 90ft

We know that,

Area of a square = side ×side

Hence, Area of the square park  = 90 × 90 = 8100 ft2

Thus, the area of a square park whose side is 90 ft is 8100 ft2

RECTANGLE:

Area = length x width

Area = l × w

Example : 

The length and width of a rectangular farm are 80 yards and 60 yards. Find the area of the farm.

Solution:

Length of the farm, l = 80 yd and width of the farm, w = 60 yards

Area of the farm A is: A = l × w

= 80 yd × 60 yards

= 4800 square yards

Therefore, the Area of the farm is 4800 square yards.

CIRCLE:

Area = π × radius × radius

Area =  π × r^2

(π = 3.14)

Real life examples: 

• To cover the floor with tiles, to cover the wall with paint or wallpaper or building a swimming pool are other examples, where the area is computed.

To determine the size of the carpet to be bought, we often find the area of the room floor.

In reality, not every plane surface can be clearly classified as a rectangle, square or a triangle. For finding the area of a composite figure that contains more than one shape, we will find the sum of the area of all the shapes forming the composite figure

FORMULAS:

Important Notes on Area of Square

Note the following points which should be remembered while we calculate the area of a square.

• A common mistake that we tend to make while calculating the area of a square is doubling the number. This is incorrect! Always remember that the area of a square is side × side and not 2 × sides.

• When we represent the area, we should not forget to write its unit. The side of a square is one-dimensional and the area of a square is two-dimensional. Hence, the area of a square is always represented as square units. For example, a square with a side of 3 units will have an area of 3 × 3 = 9 square units.

Difference between area and perimeter:

QUIZ TIME:

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