The surface area of a triangular prism can be calculated by adding the area of the two triangular faces and the area of the three rectangular faces.
First, calculate the area of the triangular faces:
Area = 0.5 * base * height
Area = 0.5 * 8.9 cm * 5 cm
Area = 22.25 square centimeters
Next, calculate the area of the rectangular faces:
Area = perimeter * height
Area = (8.9 + 15.9 + 16.7) cm * 5 cm
Area = 41.5 cm * 5 cm
Area = 207.5 square centimeters
Now, find the total surface area of the triangular prism:
Total surface area = 2 * triangular face area + 3 * rectangular face area
Total surface area = 2 * 22.25 square centimeters + 3 * 207.5 square centimeters
Total surface area = 44.5 square centimeters + 622.5 square centimeters
Total surface area = 667 square centimeters
Since one package of stickers covers 75 square centimeters, divide the total surface area by 75 to find the number of packages needed:
667 square centimeters / 75 square centimeters per package ≈ 8.9 packages
Therefore, 9 packages of stickers need to be purchased to cover the door stopper.