CBSE Class 8CBSE
Share
Notifications

View all notifications

Area of a General Quadrilateral

Login
Create free account


      Forgot password?

description

  • Triangulation
  • Area of special quadrilaterals

notes

A) Triangulation :
A general quadrilateral can be split into two triangles by drawing one of its diagonals. This “triangulation” helps us to find a formula for any general quadrilateral.

Area of quadrilateral ABCD
= ( area of Triangle ABC )+(area of Triangle ADC)

`=  (1/2 xx AC xx h_1 )` + `(1/2 xx  AC  xx  h_2 )`

`= 1/2  xx AC  xx (h_1+h_2 )`

`=1/2 d ( h_1 + h_2 )` where d denotes the length of diagonal AC.

B) Area of Special quadrilaterals :

We can use the same method of splitting into triangles (which we called “triangulation”) to find a formula for the area of a rhombus.
ABCD is a rhombus. 
Therefore, its diagonals are perpendicular bisectors of each other.

Area of rhombus ABCD
= (area of D ACD) + (area of D ABC)
`= (1/2 xx AC xx  OD)` + `(1/2 xx AC xx OB)`
`=1/2 xx AC` × `(OD + OB)`
`=1/2 xx AC xx BD`
`=1/2 d_1 × d_2`                  where AC = `d_1` and BD = `d_2`

In other words, area of a rhombus is half the product of its diagonals.

S
View in app×