Question 247152
area of a triangle equals 1/2 * b * h


from your triangle, I don't think we can find the base very easily.


fortunately there is a formula that allows you to find the area of a triangle when you only know the sides.


It's called Heron's formula.


that formula is:


Area of a Triangle = sqrt((s*(s-a)*(s-b)*(s-c)),


where s=(a+b+c)/2 which is the same as p/2 where p equals the perimeter of the triangle.


assuming that c is the base of the triangle, Heron's formula allows us to find the height of the triangle as well.


That formula would be:


h = (2 * (SQRT(s(s-a)(s-b)(s-c))) / 2


I believe this comes from the fact that A = 1/2 * b * h, so if we solve for h, we get h = 2*A/b


In your triangle:


s = (5+6+7)/2 = 18/2 = 9


In your triangle:


A = sqrt(9 * (9-5) * (9-6) * (9-7)) which equals:


sqrt (9 * 4 * 3 * 2) which equals:


sqrt (216) which equals:


14.69693846


Since A = 14.69693846, then h = 2/c * 14.69693846 = 2/7 * 14.69693846 = 4.199125273


If A = 1/2 * b * h, then A = 1/2 * 7 * 4.199125273 = 14.69693846 which is back where we started from.


You can check Heron's formula for yourself by selecting the following link.


<a href = "http://mste.illinois.edu/dildine/heron/triarea.html" target = "_blank">http://mste.illinois.edu/dildine/heron/triarea.html</a>