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)
Responses
You will need 7 packages of stickers.
You will need 7 packages of stickers.
You will need 5.5 packages of stickers.
You will need 5.5 packages of stickers.
You will need 414.14 cm2 packages of stickers.
You will need 414.14 cm squared packages of stickers.
You will need 6 packages of stickers.
You will need 7 packages of stickers.
To find the surface area of the triangular prism, you can calculate the total area of each face and then add them up.
One triangular face: (1/2) * 8.9 * 5 = 22.25 cm²
The other triangular face: (1/2) * 8.9 * 16.7 = 74.615 cm²
The rectangular face: 8.9 * 15.9 = 141.51 cm²
Total surface area = 22.25 + 74.615 + 141.51 = 238.375 cm²
Since one package of stickers covers 75 cm², you would need 4 packages to cover 300 cm², which is the closest number greater than 238.375. So you would need 4 packages at the minimum, but since you can only purchase whole packs, you would need to purchase 4 + 3 = 7 packages of stickers.