Respuesta :
Answer:
The area of triangle formed by given side lengths is 13724.27.
Step-by-step explanation:
A triangle can be formed If the sum of the other two sides (except largest side) is greater than the largest side that is a+b>c.
Here, given side lengths:
a = 240
b = 121
c = 302
Here, largest side is c = 302
so taking sum of other two sides,
a+b = 240+121 = 361> 302
Hence, triangle can be formed with a, b and c as given lengths.
Calculating area using Heron's formula,
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter
Formula to find semi perimeter is
[tex]s=\frac{a+b+c}{2}[/tex]
So, first we find the semi perimeter by using given sides,
[tex]s=\frac{240+121+302}{2}[/tex]
[tex]s=\frac{663}{2}[/tex]
[tex]s=331.5[/tex]
Now put the value of s,a,b and c in the Heron's formula,
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]Area=\sqrt{331.5(331.5-240)(331.5-121)(331.5-302)}[/tex]
[tex]Area=\sqrt{331.5\times91.5\times210.5\times29.5}[/tex]
[tex]Area=\sqrt{188355689.438}[/tex]
[tex]Area=13724.2737308[/tex]
Therefore, the area of triangle is approx. 13724.27.
