Question

Compute the area of the triangle (round to the nearest integer).

Answer 1

The Area Formula of a triangle given the coordinates of its vertices

(x1, y1), (x2, y2) and (x3, y3) is :

$A=\frac{1}{2}\lvert x_1\mleft(y_2-y_3\mright)+x_2\mleft(y_3-y_1\mright)+x_3\mleft(y_1-y_2\mright)\rvert$

From the problem, the vertices are :

$\begin{gathered} (x_1,y_1)\rightarrow(5,15) \\ (x_2,y_2)\rightarrow(20,10) \\ (x_3,y_3)\rightarrow(15,5) \end{gathered}$

Using the formula above, the area is :

$\begin{gathered} A=\frac{1}{2}\lvert x_1\mleft(y_2-y_3\mright)+x_2\mleft(y_3-y_1\mright)+x_3\mleft(y_1-y_2\mright)\rvert \\ A=\frac{1}{2}\lvert5\mleft(10-5\mright)+20\mleft(5-15\mright)+15\mleft(15-10\mright)\rvert \\ A=\frac{1}{2}\lvert5\mleft(5\mright)+20\mleft(-10\mright)+15\mleft(5\mright)\rvert \\ A=\frac{1}{2}\lvert25-200+75\rvert \\ A=\frac{1}{2}\lvert-100\rvert \\ A=50 \end{gathered}$

The answer is 50 square units