#### 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.**