Question

Find the area of the quadrilateral whose vertices are $A(1,1)B(7,-3),C(12,2)$ and $D(7,21)$

Answer 1

Area of quadrilateral ABCD=Area of triangle ABC+Area of triangle ACD

Area of triangle ABC$=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$=\frac{1}{2}\left[1\right(-3-2)+7(2-1)+12(1-(-3)\left)\right]$

$=25squnits$

Area of triangle ACD$=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$=\frac{1}{2}\left[1\right(2-21)+12(21-1)+7(1-2\left)\right]$

$=107squnits$

Area of quadrilateral ABCD$=25+107$

$=132squnits$