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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.

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.

click on the content to continue..

Consider the triangle given in the figure. The base is 13cm and height is 8cm. 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. 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. 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. 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. 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. 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,

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 2cm and height 3cm?

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

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

slide-show version coming soon