To find the area of triangle DEF, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is:
A = sqrt(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, defined as:
s = (a + b + c)/2
In this case, we have:
a = DE = 2.12
b = EF = 6
c = DF = 7.65
The semiperimeter is:
s = (a + b + c)/2 = (2.12 + 6 + 7.65)/2 = 7.885
Therefore, the area of triangle DEF is:
A = sqrt(s(s-a)(s-b)(s-c)) = sqrt(7.885(7.885-2.12)(7.885-6)(7.885-7.65)) = 9.63
The area of triangle DEF is approximately 9.63 square units.