How do you find the area of a triangle with the value of each edge, but not the height?

Question

The triangle is 330x270x240.
I don't know how to do it without a height value, It's ok if you solve the problem, but I'd really just like to know the formula.

Answer 1

perimeter = 330 + 270 + 240 = 840
semi-perimeter = s = 840/2 = 420

Sides: a = 330, b = 270, c = 240

The formula for area of a triangle whose sides are a,b,c is
sqrt[s*(s-a)(s-b)(s-c)]

Putting the values of s,a,b,c we get the area
sqrt[420*(420 - 330)(420 - 270)(420 - 240)]
= sqrt[420*(90)(150)(180)]
= sqrt[120600000]
= 31946.83

Answer 2

Area = sq rt [s(s-a)(s-b)(s-c)] where s =(a+b+c)/2 and a, b and c are the sidesof the triangle
a=330, b=270, c=240
s=(330+270+240)/2 = 840/2=420
sustitute and get the numerical value

Answer 3

There are several ways. The 1 I use is:
use the law of sines to find the angles A/sin a =B/sin b=C/sin c where A, B, & C are the sides & a, b, c are the angles opposite them, & that a+b+c=180.

Having this, you can use trig to construct the height & then A=(1/2)bh.

Answer 4

1.find the semi perimeter=(a+b+c+)/2
here in this case (330+270+240)/2=420
2.find the product of s(s-a)(s-b)(s-c)
here 420(420-330)(420-270)(420-240)
=420*90*150*180
3.find the square root of the above
{s(s-a)(s-b)(s-c)]^1/2
here rt 420*90*150*180=31950 square units

Answer 5

You need the height of the triangle to find the area. (A= .5bh) If it's a right triangle, you do know the height. If not, you need to use the trig functions (SOHCAHTOA) in order to find it.

Answer 6

For this problem you will have to apply Heron's Formula.

a,b,c sides

SemiPerimeter = s = 1/2(a+b+c)

Area = SQRT[ s * (s - a) * (s - b) * (s - c)]

That's it.

Answer 7

It would really help if you took trigonometry. Sounds like homework.