Final answer:
To calculate the area of ∆LMN, the formula ½ × base × height × sin(angle) is used. The area calculated with given values rounded to the nearest tenth is approximately 3.6 square centimeters, which does not match any of the provided options.
Step-by-step explanation:
The area of ∆LMN can be calculated using the formula for the area of a triangle when the lengths of two sides and the measure of the included angle are known: area = ½ × base × height × sin (∠). In this case, since we have the measure of ∠N, side l will be the base and side m will be the height. Therefore, the area is:
area = ½ × 3.9 cm × 2.7 cm × sin(133°).
Using a calculator, the sine of 133° is approximately 0.6820. Now we can calculate:
area = ½ × 3.9 cm × 2.7 cm × 0.6820 ≈ 3.6 square centimeters.