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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

To measure a length, area, or volume one of the following methods is used.

 •  Measurement by Superimposition

 •  Measurement by Calculation

 •  Measurement by Equivalence

The First two methods, "superimposition" and "calculation" are simple. Let us review them quickly. These two do not need much explanation and quite easy to understand.

This topic covers the measurement by superimposition.



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Consider the shape given in the figure. It is a rectangle of length `7cm` and width `5cm`. The figure also provides the reference unit-square on the right.area by superimposition What is the area of the shape?

  • `35cm^2`
  • `35cm^2`
  • area cannot be found using the given information

The answer is "`35cm^2`". The area is computed by creating a grid of unit-squares. The number of unit squares contained within the shape is the area of the rectangle.
area by superimposition

Area of the given shape is calculated by superimposing the reference unit-squares. area by superimposition. Based on this, the area of a square or rectangle is simplified to the formulas

`text(Area of a square ) = text( side)^2`

`text(Area of a rectangle ) = text( length ) xx text( width)`

Consider the shape given in the figure. The measurements are not provided. The reference unit-square is shown on the top-right corner.area by approximation What is the area of the given shape?

  • area cannot be calculated
  • approximate area can be calculated by superimposing a grid of unit-squares
  • approximate area can be calculated by superimposing a grid of unit-squares

The answer is "approximate area can be calculated by superimposing a grid of unit-squares".

The area is approximately `15cm^2`.
area of a shape.
The area is approximated to the count of large squares within the figure.

Measurement by superimposition provides accurate results for

 •  area of squares and rectangles : The unit-square has `90^@` angles at the vertices. And so, the unit-square fits within Squares and Rectangles.
area


 •  volume of cubes and cuboids : The unit-cube has `90^@` angles at the vertices. And so, the unit-cube fits within cubes and cuboids.
volume
For shapes like triangles or prisms, measurement requires some geometrical calculation or the measurement will be approximate.
area approximation

Measurement by Superimposition : Length, Area, or Volume can be measured by superimposition of corresponding unit-measures.area by superimposition This method suits best for

 •  area of squares and rectangles

 •  volume of cubes and cuboids

                            
slide-show version coming soon