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Thought-Process to Discover Knowledge

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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
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


In this page, the formula to find perimeter and area of various quadrilaterals is introduced.



click on the content to continue..

What is a parallelogram? parallelogram introduction

  • a quadrilateral with two pairs of parallel sides
  • a quadrilateral with two pairs of parallel sides
  • not a quadrilateral

The answer is "a quadrilateral with two pair of parallel sides"

Consider the parallelogram with base `8cm` and height `6cm`. The parallelogram is shown in the figure.area of a parallelogram 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`. area of a parallelogram 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?trapezium introduction

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

The answer is "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.area of a trapezium 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`. area of a trapezium 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 construction introduction

  • a quadrilateral with two pairs of equal and adjacent sides
  • a quadrilateral with two pairs of equal and adjacent sides
  • kite is not a quadrilateral

The answer is "a quadrilateral with two pair of equal and adjacent sides"

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