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 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.
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You will need 6 packages of stickers.
To find the surface area of the triangular prism, we first need to find the area of the triangular face. This can be calculated using the formula: Area = 0.5 * base * height.
Area = 0.5 * 8.9 * 5 = 22.25 cm2.
Then, we find the lateral surface area of the prism by finding the perimeter of the base and multiplying it by the slant height.
Perimeter of base = 8.9 + 5 + 16.7 = 30.6 cm.
Lateral surface area = 30.6 * 15.9 = 486.54 cm2.
Total surface area = 2 * (22.25) + 486.54 = 530.04 cm2.
Since one package covers 75 cm2, we need to divide the total surface area by the area covered by one package: 530.04 / 75 = 7.07.
Therefore, we need to purchase 7 packages of stickers to cover the surface area of the door stopper.