Final answer:
The perimeter and area of triangle ABC require more information than provided to be calculated. With angles A and C known, and side AB given, additional measurements are needed to determine perimeter and area.
Step-by-step explanation:
To solve for the perimeter of triangle ABC and its area, we first note that the sum of angles in a triangle is 180°. Given m∠A = 60° and m∠C = 45°, we find m∠B by subtracting the sum of m∠A and m∠C from 180°:
m∠B = 180° - (m∠A + m∠C) = 180° - (60° + 45°) = 75°
To find the perimeter of △ABC, we need the lengths of all three sides. Since only one side AB = 8 is given, and we have the measures of angles A and C but not their opposite sides, we cannot determine the exact perimeter without additional information such as the height or the lengths of the other sides.
To calculate the area of △ABC, the formula is:
Area = ½ × base × height
Again, we would need additional information to solve for the area, as the height correlating to the base is unknown in this case.
Without additional information, the problem cannot be solved conclusively. We need either the length of the other sides or other pertinent measurements such as the altitude for a complete solution.