Well I cant draw a determinant in this format. Otherwise it was very simple to explain. Any way I will try to explain in words only.
In your case:
Assume first figure in each bracket as x-coordinate ( along with the individual sign ), and the second figure as y-coordinate ( along with the individual sign ). Thus
x1 = 1, x2 = 6 and x3 = 2. Similarly y1 = 1, y2 = 6 and y3 = 10
Then draw up a 3x3 determinant in which arrange x1, x2, x3 in First column, similarly y1, y2, y3 in the second column and put 1 , 1, 1 in the third column.
Then if D is the value of this determinant, the required area of the triangle will be half of it. Symbolically,
A = 1/2. D
In this case you get D = 40 units and Area = D/2 = 40/2 = 20 sq units...................... Answer