Hello,
It is helpful to first draw this triangle in a rectangular coordinate system. Recall that the formula for the area of a triangle is A = (1/2)bh, where b is the "base" and h is the "height". For convenience, label the points as A(2,1), B(6,1), and C(4,9). We see that A and B lie along the horizontal line y = 1. Take the segment AB to be the base. It is then easy to see that b = 4. Then the height (or altitude) is the perpendicular distance from the vertex C to the line segment AB. This distance is 8 (i.e., h = 8). Therefore,
A = (1/2)*4*8 = 16.
The area is 16. Hope that helps.
William
