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An illustration shows a 3 D right 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.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

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 two triangular faces and the three rectangular faces.

The area of the two triangular faces can be calculated as:

1/2 * base * height = 1/2 * 8.9 cm * 5 cm = 22.25 cm^2 (for each triangular face)

The area of the three rectangular faces can be calculated as:

Length * height = 15.9 cm * 16.7 cm = 265.53 cm^2 (for each rectangular face)

So the total surface area of the triangular prism is 2 * 22.25 cm^2 + 3 * 265.53 cm^2 = 837.09 cm^2

Since one package of stickers covers 75 cm^2, you will need 837.09 cm^2 / 75 cm^2 = 11.1613 packages of stickers. Since stickers can only be purchased in whole packs, you will need to purchase 12 packages of stickers to cover the surface area of the door stopper.