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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 VolumeMensuration: Two Dimensional Shapes

### Perimeter and Area of Various Quadrilaterals

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

•  what is measurement standard?

•  Absolute and Derived Standards

click on the content to continue..

What is a parallelogram?

• a quadrilateral with two pairs of parallel sides
• a quadrilateral with two pairs of parallel sides

Consider the parallelogram with base 8cm and height 6cm. The parallelogram is shown in the figure. What is the area of the parallelogram?

Note: To find area of polygons, consider them as combination of triangles.

• area cannot be computed
• text( area )= text( base ) xx text( height)
• text( area )= text( base ) xx text( height)

The answer is "text( area )= text( base ) xx text( height)". Derivation of the formula is given in the next page.

The parallelogram ABCD is considered to be two triangles /_\ABC and /_\ACD. The area of parallelogram

=  sum of area of the two triangles

= 1/2 xx bar(AB) xx bar(PD) + 1/2 bar(CD) xx bar(PD)

in a parallelogram the opposite sides are equal bar(AB)=bar(CD)
= bar(AB) xx bar(PD)

text( area )= text( base ) xx text( height)

What is a trapezium?

• A parallelogram with two pairs of parallel sides
• A quadrilateral with one pair of parallel sides
• A quadrilateral with one pair of parallel sides

Consider the trapezium with two bases 8cm & 5cm, and height 6cm. The trapezium is shown in the figure. What is the area of the trapezium?

To find area of polygons, consider them as combination of triangles.

• area cannot be computed
• text( area )= 1/2 xx text( sum of bases ) xx text( height)
• text( area )= 1/2 xx text( sum of bases ) xx text( height)

The answer is "text( area ) = 1/2 xx text( sum of bases ) xx text( height)". Derivation of the formula is given in the next page.

The trapezium ABCD is considered as two triangles /_\ABC and /_\ACD. The area of trapezium

=  sum of area of the two triangles

= 1/2 xx bar(AB) xx bar(PD) + 1/2 bar(CD) xx bar(PD)

= 1/2 xx (bar(AB) + bar(CD)) xx bar(PD)

text( area ) = 1/2 xx text( sum of bases ) xx text( height)

What is a kite?

• kite is not a quadrilateral

Consider the kite with two diagonals 8cm and height 5cm. The kite is shown in the figure. What is the area of the kite?

• area cannot be computed
• text( area )= 1/2 xx text( product of diagonals)
• text( area )= 1/2 xx text( product of diagonals)

The answer is "text( area )= 1/2 xx text( product of diagonals)". Derivation of the formula is given in the next page.

The kite ABCD is considered to be two triangles /_\BDA and /_\BDC. The area of kite

=  sum of area of the two triangles

= 1/2 xx bar(BD) xx bar(AO) + 1/2 bar(BD) xx bar(OC)

= 1/2 xx bar(BD) xx (bar(AO) + bar(OC))

= 1/2 xx bar(BD) xx bar(AC)

text( area )= 1/2 xx text( product of the diagonals)

Area of Some Quadrilaterals : Consider the polygon shapes as combination of triangles and find sum of area of the triangles.

text( area of a parallelogram )= text( base ) xx text( height)

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

text( area of a kite )= 1/2 xx text( product of the diagonals)

Solved Exercise Problem:

What is the area of a parallelogram of 2cm length and 4cm height?

• 4cm^2
• 8cm^2
• 8cm^2

The answer is "8cm^2".

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