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# Area of a General Quadrilateral

#### description

• Triangulation

#### 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 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.

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