中二級或中三級的數學題

2011-04-14 8:10 am

圖片參考:http://imgcld.yimg.com/8/n/HA06562661/o/701104140001813873426040.jpg




我想問有什麽方法可以不要填補法都可以計算到以上的三角型的面積

想知BC幾多距離。高度幾多

教我最快的方法計算出來

是否有什麽的公式?


更新1:

講中文OK?

回答 (2)

2011-04-15 5:29 pm
✔ 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
2011-04-21 8:30 pm
用中二,中三的程度教你吧:
公式(可照抄): ∵CQ=AQ
2 + 6 5+(-7)
∴Q=(----- , -----)=(4 , -1)
2 2 設BQ為一條直線,
BQ=√(-9-2)^2+(2+(-7)^2
=12.1(答案取至三位有效數字)
AC=√(2-6)^2+(-7-5)^2
=12.7(答案取至三位有效數字)
∴△ABC的面積
= (12.7 x 12.1)÷2
=76.9(答案取至三位有效數字)


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