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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 7 packages of stickers.
You will need 7 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 6 packages of stickers.
You will need 6 packages of stickers.

You will need 5.5 packages of stickers.
You will need 5.5 packages of stickers.
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Answer 1

You will need 6 packages of stickers.

To find the surface area of the wooden door stopper, we need to calculate the total surface area of the triangular prism.

The formula for the surface area of a triangular prism is:

2 * (base * height of triangle) + (perimeter of triangle * height of prism)

Plugging in the values:

2 * (8.9 cm * 5 cm) + (8.9 cm + 16.7 cm + 15.9 cm) * 5 cm
= 2 * (44.5 cm²) + (41.5 cm) * 5 cm
= 89 cm² + 207.5 cm²
= 296.5 cm²

So, the closest number to the surface area of the door stopper is 300 cm². Since each package of stickers covers 75 cm², you will need 300 cm² / 75 cm² = 4 packages of stickers. Since stickers are only sold in whole packs, you will need to purchase 5 packages of stickers in total.

Answer 2

a b c or d

Answer 3

The correct response is:

c) You will need 6 packages of stickers.