Final answer:
The area of ΔPQR is approximately 47087 cm².
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 0.5 × base × height.
In this case, we are given one angle and two side lengths, so we can use the formula A = 0.5 × q × r × sin(P), where q and r are the given side lengths, and P is the given angle.
Plugging in the values, we get A = 0.5 × 590 cm × 310 cm × sin(24°).
Using a calculator, we find that sin(24°) ≈ 0.4067. Multiplying this value by the side lengths gives us A ≈ 47086.9 cm².
Rounding to the nearest square centimeter, the area of ΔPQR is approximately 47087 cm².