Question

Find the area of the quadrilaterals, the coordinates of whose vertices are
$(1,2),(6,2),(5,3)$ and $(3,4)$

Answer 1

Formula:

Area of quadrilateral$=$ area of triangle $1$ $+$ area of triangle $2$

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

Given,

$A(1,2),B(6,2),C(5,3),D(3,4)$

Let the first triangle be, ABC

Area of $△ABC=\frac{1}{2}\left[1\right(2-3)+6(3-2)+5(2-2\left)\right]$

$=\frac{1}{2}[-1+6+0]$

$=\frac{5}{2}$sq.units

Area of $△ACD=\frac{1}{2}\left[1\right(3-4)+5(4-2)+3(2-3\left)\right]$

$=\frac{1}{2}[-1+10-3]$

$=3$sq.units

Area of quadrilateral $=\frac{5}{2}+3=\frac{11}{2}$sq.units