To find area of any general quadrilateral,

We split it into triangles and add their area parallelogram has opposites sides equal & parallel

For Quadrilateral ABCD

We join AC

So, we have two triangles - Δ ADC and Δ ABC

Let h
_{
1
}
be height from point D to AC

& h
_{
2
}
be height from point B to AC

So,

Area of Quadrilateral ABCD

= Area of Δ ADC + Area of Δ ABC

= 1/2 × AC × h
_{
1
}
+ 1/2 × AC × h
_{
2
}

= 1/2 × AC × (h
_{
1
}
+ h
_{
2
}
)

**
=
**
**
1/2
**
**
×
**
**
d
**
**
(h
**
_{
1
}
**
+ h
**
_{
2
}
**
)
**

where d = Length of Diagonal

Find area of quadrilateral ABCD

Given

Length of diagonal = d = 10 cm

Length of Perpendicular dropped on AC

h
_{
1
}
= 5 cm

& h
_{
2
}
= 3 cm

Now,

Area of ABCD = d/2 (h
_{
1
}
+ h
_{
2
}
)

= 10/2 (5 + 3)

= 10/2 × 8

= 5 × 8

= 40 cm
^{
2
}

Area of quadrilateral =
**
40 cm
**
^{
2
}
**
**