✔ 最佳答案
If the three sides of a triangle are known, a, b, c
Using Heron Formula:
Area of triangle = √ [ s (s - a) (s - b) (s - c) ] ,
where s = (a+b+c)/2 [semi-perimeter]
Find the length of AB, AC, BC
Distance between 2 points is given by √[ (x2 – x1)^2 + (y2-y1)^2]
where coordinates of two points are (x1, y1) and (x2, y2)
A(6, 5), B(-9, 2), C(2, -7)
AB = 15.297
AC = 12.6491
BC = 14.21267
s = (15.297 + 12.6491 + 14.21267)/2
s = 21.0794
Area = √ [ s (s - a) (s - b) (s - c) ]
Area = √ [21.0794 (21.0794 - 14.21267) (21.0794 - 12.6491) (21.0794 - 15.297) ]
Area = 84
Area = (BC x AD)/2 where AD is the height, AD is perpendicular to BC
84 = (14.21267 x AD)/2
AD = 2x84/14.21267 = 11.82
Area = 84, BC = 14.21, AD (height) = 11.82
(accurate to 2 decimal)
Another method is long-winded:
First find the coordinate of point D,
Find the slope BC, then slope AD, linear equations of line BC and line AD
Find the intersection of these 2 lines, hence you find coordinate of D
Find length AD, length BC, and area = base x height/2
