o 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 total surface area of the triangular prism.
First, we find the area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 8.9 cm * 5 cm
Area = 22.25 square centimeters
Next, we find the area of the rectangular faces:
Area = length * height
Area = 15.9 cm * 5 cm
Area = 79.5 square centimeters (for each rectangular face)
Total area = 2 * 79.5 square centimeters
Total area = 159 square centimeters
Now, we add the area of the triangular face to find the total surface area:
Total surface area = 22.25 square centimeters + 159 square centimeters
Total surface area = 181.25 square centimeters
Since one package of stickers covers 75 square centimeters, we divide the total surface area by 75 to find out how many packages of stickers need to be purchased:
181.25 square centimeters / 75 square centimeters = 2.42
Since we can only purchase whole packs of stickers, we need to round up to the nearest whole number. Therefore, 3 packages of stickers need to be purchased to cover the door stopper.