To find the area of triangle VWX, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we have two sides and the included angle, so we can use the formula:
Area = (1/2) * VW * WX * sin(V)
First, let's calculate the lengths of sides VW and WX using the law of sines:
VW / sin(X) = WX / sin(V)
VW / sin(80°) = WX / sin(32°)
VW = (WX * sin(80°)) / sin(32°)
Now, substitute the value of VW in the area formula:
Area = (1/2) * [(WX * sin(80°)) / sin(32°)] * WX * sin(V)
Area = (1/2) * WX^2 * (sin(80°) * sin(V)) / sin(32°)
Area = (1/2) * WX^2 * (sin(80°) * sin(32°)) / sin(32°)
Area ≈ (1/2) * WX^2 * 0.7365 (rounded to four decimal places)
Now, substitute the value of WX and calculate the area:
Area ≈ (1/2) * (680 cm)^2 * 0.7365
Area ≈ 139,850.4 cm^2
Therefore, the area of triangle VWX is approximately 139,850.4 square centimeters to the nearest 10th of a square centimeter.