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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 VolumeIntroduction to Measurements

### Introduction to Measuring Area

This topic introduced measuring area as "surface-span". It is a derived standard and measured in reference to a standard 1x1 square.

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The length of a rod is the distance-span measured in meter.

For a surface of some shape (like a paper, or a leaf), what is the measure of the surface?

• length measurement between various points
• area is the surface-span of a surface
• area is the surface-span of a surface

The answer is "area is the surface-span of a surface"

To specify distance-span or length, a reference-prototype-standard (ie a metal rod of specific material at specific temperature) was defined. Any length measurement is specified in reference to the prototype-standard.

Which of the following helps to specify a surface-span?

• to specify area, a reference-prototype-standard has to be defined
• measurement of area can be derived from the already defined measure of length
• measurement of area can be derived from the already defined measure of length

The answer is "measurement of area can be derived from the already defined measure of length"

To specify the surface-span or area of a surface, a square of side 1 meter is taken as the reference. The area of that is one square meter or 1m^2. In the figure this is shown in the top right corner. Area of a surface is given in reference to the area of a square of side 1 meter. In the figure, the area of the given rectangle is the number of 1 square meter squares fit in that rectangle. It is counted to 6, so the area of the rectangle is 6m^2.

Area of a plane figure : The surface-span of a plane figure is the area of the surface. It is measured in square meter (or in one of other derived or similar forms). Area is specified as a number in reference to the surface-span of a square of 1 meter side.

Which of the following explains the statement "area of the paper is 3 square meter"?

• it is just area
• The surface-span of the paper equals 3 surface-spans of a square of side 1 meter
• The surface-span of the paper equals 3 surface-spans of a square of side 1 meter

The answer is "The surface-span of the paper equals 3 surface-spans of a square of side 1 meter".

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