Area

 Objective:

This topic gives an overview of 

  • Area
  • Area of Rectangle
  • Area of Square

Area

In mathematics the area of a plane figure refers to the number of square units the figure covers. The area is the inside shape or space measured in square units. In rectangles and in squares, a simple calculation of length and width will give the number of square units. The square units could be inches, centimeters, yards etc. or whatever the requested unit of measure asks for. There are many formulas used to determine the area of many common shapes or polygons. The amount of surface enclosed by a closed figure is called its area.

The following conventions are to be adopted while calculating the area of a closed figure using a squared or graph paper.

  • Count the fully-filled squares covered by the closed figure as one square unit or unit square each.
  • Count the half-filled squares as half a square unit.
  • Count the squares that are more than half-filled as one square unit.
  • Ignore the squares filled less than half.

For example, the area of this shape can be calculated as shown:

Covered area Number Area estimate (sq. units)
Fully filled squares 6 6
Half–filled squares 7 7 x ½
Squares filled more than half 0 0
Squares filled less than half 0 0

Area covered by full squares = 6 x 1 = 6 sq. units.

Area covered by half squares = 7 x ½ = 7/2= 3 ½ sq. units

Total area of the given shape = 6 + 3 ½ sq. units

Thus, the total area of the given shape = 9 ½ sq. Units

Area of a rectangle can be obtained by multiplying length by breadth. Area of the square can be obtained by multiplying side by side.

Area of a Rectangle

The area of a polygon is the number of square units inside the polygon. To understand the difference between perimeter and area, think of perimeter as the length of fence needed to enclose the yard, whereas area is the space inside the yard. Perimeter is 1-dimensional and is measured in linear units such as inches, feet or meters. Area is 2-dimensional: it has a length and a width. Area is measured in square units such as square inches, square feet or square meters.  

To find the area of a rectangle, multiply the length by the width. The formula is:

Area of a rectangle = (length × breadth)

Let's look at some examples of finding the area of rectangles.

Example 1:  A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the area.  

Solution: A = L.W

A = (8 cm) · (3 cm) = 24 cm 2

In Example 1, we found the area given the dimensions of the rectangle. Let's look at some examples in which we are given the area of the rectangle, and are asked to work backwards to find the missing dimension.

 Example 2: The area of a square is 9 square centimeters. How long is one side?  

Solution:  A = s.s

9 cm 2 = s · s

Since 3 · 3 = 9, we get 3 cm · 3 cm = 9 cm2. So S must equal 3 cm.

S=3 cm

Area of a Square

A Square is a flat shape with 4 equal sides and every angle is a right angle (90°). All sides are equal in length.

To figure out the area of a square, you multiply the length by the width. Because the length and the width are always the same, you could also say that you square the length of any one side of the square (that's why they call it the "square"). 

Area of the square = side × side

Example 1: Find the area of a square plot of side 8 m.

Solution: Side of the square = 8 m

Area of the square = side × side = 8 m × 8 m = 64 sq m.

Summary

  • The amount of surface enclosed by a closed figure is called its area.
  • Area of a rectangle can be obtained by multiplying length by breadth.
  • The dimensions of a rectangle are length and width.
  • Given the length and width of a rectangle, we can find the area.
  • Given the area and one dimension of a rectangle, we can find the other dimension.
  • Area of the square can be obtained by multiplying side by side.

 

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