In the triangle AOB, the coordinates of two points AB are (- 4, - 6), (- 6, - 3) respectively, and the area of the triangle can be calculated (hint: the area of the triangle AOB can be seen from

In the triangle AOB, the coordinates of two points AB are (- 4, - 6), (- 6, - 3) respectively, and the area of the triangle can be calculated (hint: the area of the triangle AOB can be seen from

S=1/2*0A*OB*sin∠AOB=1/2*(OA^+OB^-AB^)/(2*OA*OB)*OA*OB=(OA^+OB^-AB^)/4=21

As shown in the figure, the coordinates of a and B in △ AOB are (2,4), (6,2) respectively. Find the area of △ AOB. (the area of △ AOB can be regarded as the area of a rectangle minus the area of some small triangles.)

The intersection of CE and CF is C, and the perpendicular foot is e, f ∵ a (2,4), B (6,2) ∵ OE = AC = 4, EA = CB = BF = 2, of = 6, ∵ secfo = 6 × 4 = 24 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp (2) s △ AOE = 12 × 4 × 2 = 4 (4 points) s △ ACB = 12 × 4 × 2 = 4 & nbsp (6 points) s △ BOF = 12 × 6 × 2 = 6 & nbsp (8) s △ AOB = secfo-s △ aoe-s △ acb-s △ BOF = 24-4-4-6 = 10 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp (10 points) the AOB area is 10