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 414.14 cm2 packages of stickers.
You will need 414.14 cm squared packages of stickers.
You will need 7 packages of stickers.
You will need 7 packages of stickers.
You will need 6 packages of stickers.
You will need 6 packages of stickers.
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You will need 6 packages of stickers.
To find the surface area of the triangular prism covered by stickers, we can calculate the surface area of each of its faces and then add them up.
First, the area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 8.9 cm * 5 cm
Area = 22.25 cm²
Next, the area of the rectangular faces:
Area = base * height
Area = 8.9 cm * 15.9 cm
Area = 141.51 cm²
Now, add up the areas of the three faces:
22.25 cm² (triangular face) + 141.51 cm² (rectangle face 1) + 141.51 cm² (rectangle face 2) = 305.27 cm²
Since one package of stickers covers an area of 75 cm², divide the total surface area of the door stopper by 75:
305.27 cm² / 75 cm² ≈ 4.0709
Therefore, you will need to purchase 5 packages of stickers to cover the door stopper.