Use the image to answer the question. An illustration shows a 3-D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 15.9 centimeters and 8.9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the other side measures 16.7 centimeters. A wooden door stopper needs to be covered with stickers to match the door for a directing contest. If one package of stickers covers a surface area of 75 square centimeters, how many packages of stickers need to be purchased? (Find the closest number to the surface area of the door stopper. Stickers may only be purchased in whole packs.)
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.