Question

Find the area of the quadrilateral whose vertices are $A(2,1),B(2,3),C(-2,2)$ and $D(-1,0)$

Answer 1

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

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

Area of$△ABC=\frac{1}{2}\left[2\right(3-2)+2(2-1)+(-2\left)\right(1-3\left)\right]=\frac{1}{2}\times 8=4sq.units$

Area of$△ADC=\frac{1}{2}\left[2\right(0-2)+(-1\left)\right(2-1)+(-2\left)\right(-1-2\left)\right]=\frac{1}{2}\times 1=\frac{1}{2}sq.units$

Area of quadrilateral $ABCD=4+\frac{1}{2}=\frac{9}{2}sq.units$