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 6 packages of stickers.
You will need 414.14 cm2 packages of stickers.
You will need 7 packages of stickers.
You will need 5.5 packages of stickers.
You will need 6 packages of stickers.
To find the surface area of the door stopper, calculate the area of each face of the triangular prism separately and then add them up.
First, calculate the area of the triangular face:
Area = (1/2) * base * height = (1/2) * 8.9 * 5 = 22.25 cm²
Next, calculate the area of the rectangular face:
Area = base * height = 8.9 * 15.9 = 141.51 cm²
Since there are two rectangular faces, the total area for both rectangular faces is 2 * 141.51 = 283.02 cm²
Now, add up the areas of all three faces:
22.25 + 283.02 = 305.27 cm²
Since one package of stickers covers 75 cm², divide the total surface area of the door stopper by 75:
305.27 / 75 ≈ 4.07
You cannot purchase a fraction of a package of stickers, so round up to the nearest whole number, which is 5. Therefore, you will need to purchase 5 packages of stickers to cover the door stopper.