In order to calculate the area of the given triangle, use the Heron's formula:
A = √(s(s - a)(s - b)(s - c))
where
s = (a + b + c)/2
and a, b and c, are the lengths of the sides of the triangle. In this case, you have:
a = 5 in
b = 12 in
c = 13 in
replace the previous values of the parameters into the formula for s, and then replace the values of the parameters into the formula for the Area:
s = (5 in + 12 in + 13 in)/2 = 30 in/2 = 15 in
s = 15 in
A = √(15 in·(15 in - 5 in)(15 in - 12 in)(15 in - 13 in))
A = √(15 in·(10 in)(3 in)(2 in))
A = √(900 in⁴)
A = 30 in²
Hence, the area of the given triangle is 30 in²