Question

If a(4, 8), b(3, 4), c(0, 5) and d(5, 6) are the vertices of a quadrilateral abcd, find itsarea.

Answer 1

Answer:

Area = 9.5

Step-by-step explanation:

Use the Surveyor's Area Formula.

A quick sketch shows that the quadrilateral with these points is acbd (not abcd), so we use the points in that order.

$\displaystyle\text{Area}=\tfrac12\left(\left|\begin{array}{cc}4&8\\0&5{\end{array}\right|+\left|\begin{array}{cc}0&5\\3&4{\end{array}\right|+\left|\begin{array}{cc}3&4\\5&6{\end{array}\right|+\left|\begin{array}{cc}5&6\\4&8{\end{array}\right|\right)\\\\=\tfrac12\left(20-0+0-15+18-20+40-24\right)\\\\=\tfrac12\times19\\\\=9.5$