To find out how many packages of stickers are needed to cover the surface area of the triangular prism-shaped door stopper, we first need to calculate the total surface area of the prism.
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Find the area of the triangular face: The triangular face is a right triangle with a base (b) of 8.9 cm and a height (h) of 5 cm. The area (A) of a right triangle is given by: \[ A = \frac{1}{2} \times b \times h \] Substituting the given values: \[ A = \frac{1}{2} \times 8.9 \times 5 = \frac{44.5}{2} = 22.25 \text{ cm}^2 \]
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Find the perimeter of the triangular face: To find the total surface area, we need the perimeter of the triangular face. The sides of the right triangle are 5 cm, 8.9 cm, and 16.7 cm. Thus, the perimeter (P) is: \[ P = 5 + 8.9 + 16.7 = 30.6 \text{ cm} \]
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Calculate the surface area of the prism: The total surface area (SA) of the triangular prism can be calculated as follows: \[ SA = 2 \times A + P \times \text{length} \] The length of the prism is given as 15.9 cm. Therefore: \[ SA = 2 \times 22.25 + 30.6 \times 15.9 \] Calculating each part: \[ 2 \times 22.25 = 44.5 \] \[ 30.6 \times 15.9 = 486.54 \] So, \[ SA = 44.5 + 486.54 = 531.04 \text{ cm}^2 \]
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Determine the number of sticker packages: Each package covers 75 cm². To find the number of packages needed, divide the total surface area by the area covered by one package: \[ \text{Number of packages} = \frac{531.04}{75} \approx 7.014 \] Since packages can only be purchased in whole numbers, we round this up to the next whole number, which is 8.
Thus, the closest options based on the calculations suggest the following:
You will need 8 packages of stickers.
However, none of the provided answers reflect this, but based on the calculation, the correct answer for practical purposes is that you will need 8 packages since stickers can only be purchased in whole packs.