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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


The area of a triangle is calculated based on geometrical properties. In this chapter, the different configurations of triangles are illustrated and a common formula is derived.



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Consider the triangle given in the figure. The base is `13cm` and height is `8cm`.area of a triangle Which of the following helps to find the area of the triangle?

  • compare the triangle with a rectangle of `13cm` by `8cm` to calculate the area
  • compare the triangle with a rectangle of `13cm` by `8cm` to calculate the area
  • approximate the area using unit-squares

The answer is "compare the triangle with a rectangle of `13cm` by `8cm` to calculate the area".

The triangle of base `13cm` and height `8cm` is placed over a rectangle of length `13cm` and width `8cm`. It is noted that the triangle splits the rectangle into equal halves. area of a triangle What is the area of the triangle?

  • half of the area of rectangle
  • `1/2 xx text( base ) xx ( height)`
  • both the above
  • both the above

The answer is "both the above"

Consider the triangle given in the figure. The base is `15cm` and height is `6cm`.area of a triangle Which of the following helps to find the area of the triangle?

  • compare the triangle with a rectangle of `15cm` by `6cm` to calculate the area
  • compare the triangle with a rectangle of `15cm` by `6cm` to calculate the area
  • approximate the area using unit-squares

The answer is "compare the triangle with a rectangle of `15cm` by `6cm` to calculate the area"

The triangle of base `15cm` and height `6cm` is placed over a rectangle of length `15cm` and width `6cm`.

The rectangle is visualized into two parts `ARCP` and `RBQC`

The triangle is visualized into two parts `/_\ARC` and `/_\RBC`

It is noted that the area of the triangle `/_\ARC` is half of the rectangle `ARCP` and area of the triangle `/_\RBC` is half of the rectangle `RBQC`. area of a triangle What is the area of the triangle?

  • half of the area of rectangle
  • `1/2 xx text( base ) xx ( height)`
  • both the above
  • both the above

The answer is "both the above".

The area of the triangle `/_\ABC` is sum of area of the two triangles `/_\ARC` and `/_\CRB`.

`=` half the area of rectangles `ARCP` and `CRBQ`.

`= 1/2 xx bar(AR) xx bar(RC) + 1/2 xx bar(RB) xx bar(RC)`

`= 1/2 xx bar(RC) xx ( bar(AR)+ bar(RB)) `

`= 1/2 xx bar(RC) xx bar(AB))`

`= 1/2 xx text( base )xx text( height)`

Consider the triangle given in the figure. The base is `8cm` and height is `6cm`.area of a triangle Which of the following helps to find the area of the triangle?

  • compare the triangle with a rectangle covering `AQC` to calculate the area
  • compare the triangle with a rectangle covering `AQC` to calculate the area
  • approximate the area using unit-squares

The answer is "compare the triangle with a rectangle covering `AQC` to calculate the area"

The triangle of base `8cm` and height `6cm` is placed over a rectangle `AQCP`. The rectangle is visualized to two triangles `/_\AQC` and `/_APC`. The area of triangle `/_\AQC` is half of the rectangle. area of a triangle What is the area of the triangle `/_\ABC`?

  • only a part of the area of the rectangle
  • `1/2 xx text( base ) xx ( height)`
  • both the above
  • both the above

The answer is "both the above".

The area of the triangle `/_\ABC` is

`=` area of `/_\AQC - ` area of `/_\BQC`

`= 1/2 xx bar(AQ) xx bar(QC) - ` ` 1/2 xx bar(BQ) xx bar(QC)`

`= 1/2 xx bar(QC) xx ( bar(AQ) -bar(BQ) )`

`= 1/2 xx bar(QC) xx bar(AB)`

`= 1/2 xx text( base )xx text( height)`

Consider the three types of triangles,
area of a triangle
area of a triangle
area of a triangle

For all the configurations, the area is derived as

`1/2 xx text( base ) xx ( height)`

Area of a Triangle:
`1/2 xx text( base ) xx ( height)`

Solved Exercise Problem:

What is the area of the triangle with base `2`cm and height `3`cm?

  • `2xx3=6cm^2`
  • `1/2 xx 2xx3 = 3cm^2`
  • `1/2 xx 2xx3 = 3cm^2`

The answer is "`1/2 xx 2xx3 = 3cm^2`"

                            
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