Find the area of the quadrilateral ABCD; in which AB = 7 cm; BC =6 cm;CD =12 cm; DA= 15 cm and AC =9 cm

Explanation

By Heron's Formula,`s=(a+b+c)/2`
`s=(7+6+9)/2=11cm`
Area of Triangle`=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(11(11-7)(11-6)(11-9)`
`=sqrt440cm^2`
Now in triangle ADC,s`=(15+12+9)/2=18cm`
Area`=sqrt(18(18-15)(18-12)(18-9)`
`=54cm^2`
Area of quadrilateral, `ABCD=(sqrt440+54)cm^2`