Question

The area of the quadrilateral ABCD formed by the points a(4,3),b(6,4),c(5,6),d(3,7)

Answer 1

$\text{Given points are A(4,3), B(6,4), C(5,6), D(3,7)}$

$\textbf{Area of triangle ABC}$

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

$=\frac{1}{2}[4(4-6)+6(6-3)+5(3-4)]$

$=\frac{1}{2}[4(-2)+6(3)+5(-1)]$

$=\frac{1}{2}[-8+18-5]$

$=\frac{5}{2}\;\text{square units}$

$\textbf{Area of triangle ACD}$

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

$=\frac{1}{2}[4(6-7)+5(7-3)+3(3-6)]$

$=\frac{1}{2}[4(-1)+5(4)+3(-3)]$

$=\frac{1}{2}[-4+20-9]$

$=\frac{7}{2}\;\text{square units}$

$\text{Now,}$

$\text{Area of quadrilateral ABCD}$

$=\text{Area of triangle ABC}+\text{Area of triangle ACD}$

$=\frac{5}{2}+\frac{7}{2}$

$=6\;\text{square units}$

Find more:

Find the area of a quadrilateral formed by the points (1, 0) (0, 1) (- 1, 0) and (0, - 1 )taken in order

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