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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.
mathsMensuration : Length, Area, and VolumeMeasurement Methods

### Measurement by superimposition

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.

click on the content to continue..

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. 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 of the given shape is calculated by superimposing the reference unit-squares. 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. 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.
.
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.

•  volume of cubes and cuboids : The unit-cube has 90^@ angles at the vertices. And so, the unit-cube fits within cubes and cuboids.

For shapes like triangles or prisms, measurement requires some geometrical calculation or the measurement will be approximate.

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

•  area of squares and rectangles

•  volume of cubes and cuboids

slide-show version coming soon