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 5.5 packages of stickers.
You will need 5.5 packages of stickers.
You will need 6 packages of stickers.
You will need 6 packages of stickers.
You will need 7 packages of stickers.
You will need 7 packages of stickers.
You will need 414.14 cm2 packages of stickers.
You will need 414.14 cm squared packages of stickers.
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You will need 6 packages of stickers.
To find the surface area of the triangular prism, we need to calculate the area of the triangular face and the two rectangular faces.
The area of the triangular face is (1/2) * base * perpendicular side = (1/2) * 8.9 cm * 5 cm = 22.25 cm^2.
The area of one of the rectangular faces is base * height = 8.9 cm * 15.9 cm = 141.51 cm^2.
Since there are two rectangular faces, the total area of the rectangular faces is 2 * 141.51 cm^2 = 283.02 cm^2.
Therefore, the total surface area of the triangular prism is 22.25 cm^2 (triangular face) + 283.02 cm^2 (rectangular faces) = 305.27 cm^2.
Now, divide the total surface area of the triangular prism by the surface area one package of stickers covers (75 cm^2) to find the number of packages needed: 305.27 cm^2 / 75 cm^2 ≈ 4.07.
Since stickers can only be purchased in whole packs, you will need to round up to the nearest whole number, which is 6 packages of stickers.