The area of a triangle $ ABC $ is:
$$ \Delta_{ABC} = 10 $$The area of the triangle is given by:
$$ \Delta = \left| \frac{A_x(B_y - C_y) + B_x (C_y - A_y) + C_x (A_y - B_y)}{2} \right| $$where $ A_x $ and $ A_y $ are $ x $ and $ y $ coordinates of the point $ A $ , $ B_x $ and $ B_y $ are $ x $ and $ y $ coordinates of the point $ B $ etc..
In this example we have : $ A_x = 2 $ , $ A_y = 1 $ , $ B_x = 3 $ , $ B_y = -2 $ , $ C_x = -4 $ and $ C_y = -1 $ .
When we insert these values into the formula, we obtain the given result.