__maths__>__Mensuration : Length, Area, and Volume__>__Mensuration: 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?

- 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. 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

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. 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?

- 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. 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`".

*slide-show version coming soon*