Question

Find the area of the quadrilateral `A B C D` having vertices `A(1,1),B(7,-3),C(12 ,2),` and `D(7, 21)dot`

Answer 1

Here, given points are in cyclic order. Therefore,
`Area=(1)/(2)||{:(1,,1,,),(7,,-3,,),(12,,2,,),(7,,21,,),(1,,1,,):}||`
`(1)/(2) |(-3-7)+(14+36)+(252-14) +(7-21)|`
`=132sq`. units.