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 centimeter.
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 purchase in whole packs.)
First, we need to calculate the surface area of the triangular prism (door stopper).
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2 * base area of the triangular faces + lateral area
The base area of the triangular face can be calculated using the formula for the area of a right triangle:
Base area = 0.5 * base * height
Base area = 0.5 * 8.9 * 5
Base area = 22.25 cm²
The lateral area of the prism can be calculated using the formula:
Lateral area = perimeter of the base * height
Lateral area = (8.9 + 15.9 + 16.7) * 5
Lateral area = 20.7 * 5
Lateral area = 103.5 cm²
Now, we can calculate the total surface area of the triangular prism:
Surface Area = 2 * 22.25 + 103.5
Surface Area = 44.5 + 103.5
Surface Area = 148 cm²
Since one package of stickers covers an area of 75 square centimeters and the closest number to the surface area of the door stopper is 150 cm², you would need to purchase 2 packages of stickers to completely cover the wooden door stopper.