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The coordinate plane is a basic concept in geometry. It is also commonly referred to as the  Cartesian plane. The cartesian plane is a 2 dimensional plane that is described in terms of two perpendicular axis - the horizontal x axis and the vertical y axis.

A math grid is another name for the coordinate plane consisting of a space of small squares. Each square is used as a measurement and represents 1 unit along the x and y axis.

                                                                 
The position of points on the grid are indicated by their positions along the x and y-axes thus giving us an ordered pair of numbers i.e. (x, y). The first number gives the point’s location on the grid along the x axis and the second number gives the location on the grid along the y axis.

In addition to finding the position, you can also easily find the perimeter and area of shapes using the grid.

Perimeter of a shape
The perimeter of a shape is the area around it. You can measure the perimeter by counting the number of squares in the grid.

For example: The squares on this grid are 1cm x 1cm. The length of the rectangle occupies 4 squares and its breadth occupies 1 square.

                                                               

The perimeter of the rectangle     = 2 ( l + b )
                    = 2 * ( 4 + 1 )
                    = 10 cms.

You can also easily find the perimeter of more complex shapes.
For example: The perimeter of the given shape can be easily found by counting the squares.

                                                        

Perimeter    = 3 + 4 + 1 + 1+ 2 + 3
= 14 cms                    

Area of a shape
Similarly, you can also find the area of a shape by counting the squares in the grid.
For example: The squares on this grid are 1cm x 1cm. The length of the rectangle occupies 4 squares and its breadth occupies 1 square.

                                                           

The grid covers 4 squares. So the area of the rectangle = 4 sq cms. We can also verify by using the formula:
The area of the rectangle = l * b = 4 * 1 = 4 sq cms
                    
You can also easily find the area of more complex shapes.
For example: The area of the given shape can be easily found by counting the squares.

                                                       
Area of the shape = 10 sq cms                    

Formula for Area of a triangle
You can also find the area of a triangle using the grid with the following steps:

  • First extend the triangle to make a rectangle
  • Determine the area of the rectangle by counting the squares as in the example above
  • Now divide by 2 ( half the number of squares) to get the area of the triangle 
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