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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

In the topic "mensuration", the foundation focuses on learning

 •  what is measurement standard?

 •  Absolute and Derived Standards

 •  Measurement by superimposition

 •  Measurement by calculation

 •  Measurement by equivalence (infinitesimal and Cavalieri's principle in 2D and 3D. )


In this topic, finding area of polygons is reviewed quickly.



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Consider the polygon shown in the figure.area of a polygon Which of the following help to find the area of the polygon?

  • area of a polygon cannot be calculated
  • consider the polygon as combination of triangles and find the sum of the areas of triangles
  • consider the polygon as combination of triangles and find the sum of the areas of triangles

The answer is "consider the polygon as combination of triangles"

Consider the polygon shown in the figure.area of a polygon Area of the polygon

`=` area of `/_\ABD + ` area of `/_\DBC` + area of `/_\ADE`.

The formula for area of triangle is used to find the area of the polygons.

Area of a Polygon : Consider a polygon to be combination of known geometrical forms, mostly triangles.

The geometrical forms and the formula for area are:

Area of a triangle `= 1/2 xx text( base ) xx text( height)`

Area of a trapezium `= 1/2 xx text( sum of bases ) xx text( height)`

Area of a parallelogram `= 1/2 xx text( base ) xx text( height)`

Area of a kite `= 1/2 xx text( major-diagonal ) xx text( d2)`

Solved Exercise Problem:

What is the area of a quadrilateral with all internal angles `90^@` and two sides `4cm` and `3`cm?

  • two triangles with combined area `2 xx 1/2 xx 4 xx 3 = 12cm^2`
  • area of the rectangle `4 xx 3 = 12 cm^2`
  • both the above
  • both the above

The answer is "both the above"

                            
slide-show version coming soon