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.)
You will need 6 packages of stickers.
You will need 7 packages of stickers.
You will need 414.14 cm2 packages of stickers.
You will need 5.5 packages of stickers.
To find the surface area of the triangular prism, we can calculate the area of each face individually.
The area of the triangular face (right triangle) can be calculated using the formula for the area of a triangle: 1/2 * base * height.
Area = 1/2 * 8.9 cm * 5 cm = 44.5 cm².
The area of the rectangular faces can be calculated by multiplying the length by the width:
Area = 15.9 cm * 8.9 cm = 141.51 cm² (for one face) * 2 = 283.02 cm² (for both faces).
Now add the areas of the triangular face and the two rectangular faces to find the total surface area:
Total area = 44.5 cm² + 283.02 cm² = 327.52 cm².
Since one package of stickers covers a surface area of 75 cm², we divide the total surface area of the triangular prism by 75 cm² to find out how many packages of stickers need to be purchased:
327.52 cm² ÷ 75 cm² = 4.3667.
Since stickers can only be purchased in whole packages, you will need to purchase 5 packages of stickers to cover the door stopper.
Therefore, the closest answer is: You will need 5.5 packages of stickers.