可以运用海伦公式进行计算。具体如下:
1、计算高的长度首先知道三角形的面积;
假设在平面内,有一个三角形,边长分别为a、b、c,三角形的面积S可由以下公式求得:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b2de9c82d158ccbf0f4fb96714d8bc3eb03541ff?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
注:p为半周长(周长的一半)。
2、因为
(面积=底×高÷2。其中,a是三角形的底,h是底所对应的高)
所以:
a边上的高ha= ![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/503d269759ee3d6dbb208b964e166d224e4ade8d?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
b边上的高hb= ![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/58ee3d6d55fbb2fbb3cd544f424a20a44723dc8d?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
c边上的高hc= ![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/6159252dd42a283439473a5656b5c9ea14cebf8d?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
扩展资料:
1、海伦公式:![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b21c8701a18b87d6ea65a5420a0828381f30fd4c?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
2、半周长:![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/ae51f3deb48f8c54df69cb7237292df5e0fe7f30?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
3、三角形面积的其他计算方法:
(1) ![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/ac345982b2b7d0a224250ac0c6ef76094a369afa?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
(2)
(其中,R是外接圆半径)
(3)
(其中,r是内切圆半径,p是半周长)
注:"Metrica"《度量论》手抄本中用s作为半周长,所以
和
两种写法都是可以的,但多用p作为半周长。