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.)
(1 point)
To find the surface area of the triangular prism, we need to calculate the area of the triangular faces and the area of the rectangular faces.
Area of triangular faces:
1/2 * base * height = 0.5 * 8.9 * 5 = 22.25 cm²
Area of rectangular faces:
base * height = 8.9 * 15.9 = 141.51 cm²
Total surface area:
2(triangular face area) + 3(rectangular face area) = 2(22.25) + 3(141.51) = 44.5 + 424.53 = 469.03 cm²
Now we can find the number of packages of stickers needed:
469.03 cm² / 75 cm² = 6.253…
Since stickers can only be purchased in whole packs, you would need to purchase 7 packages of stickers to cover the surface area of the door stopper.