Answer:
about 21.3 cm²
Explanation:
Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.
Area using sine formula
A = 1/2ab·sin(C)
A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units
Area using Heron's formula
The semiperimeter is ...
s = (6 +8 +12)/2 = 13
The area is ...
A = √(s(s -a)(s -b)(s -c))
A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455
A ≈ 21.33 . . . . square centimeters
The area of the triangle is about 21.3 cm².
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Additional comment
The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.
Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.
The attachment shows the solution using side lengths only.