Final answer:
To find the area of an oblique triangle with side lengths known (SSS), Heron's formula is used, which involves the semi-perimeter. For a triangle with a specific base and height, the simple formula of half the product of base and height gives the area in square millimeters or centimeters.
Step-by-step explanation:
To find the area of an oblique triangle given the lengths of all three sides (SSS), you can use Heron's formula. This formula states that the area of a triangle whose sides have lengths a, b, and c is:
Area = \( \sqrt{s(s-a)(s-b)(s-c)} \)
where \( s \) is the semi-perimeter of the triangle, calculated as \( s = \frac{a+b+c}{2} \). Now, let's apply this to find the area of a triangle with a base of 166 mm and a height of 930.0 mm. The simple formula for the area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). In this case, the area would be:
Area = \( \frac{1}{2} \times 166 \text{ mm} \times 930.0 \text{ mm} \) = \( 77190 \text{ mm}^2 \) or \( 77.190 \text{ cm}^2 \) when converting to square centimeters, with four significant figures.