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 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
a wedge of cheese is shaped like a triangular prism. how much plastic wrap is needed to cover the wedge of cheese?
240 cm^2
810 cm^2
330 cm^2
287 cm^2
To find the amount of plastic wrap needed to cover the wedge of cheese (triangular prism), we need to find the surface area of the prism. The formula for the surface area of a triangular prism is:
Surface Area = 2 * base area + lateral area
First, calculate the base area of the triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 9 * 5
Base area = 22.5 cm^2
Next, calculate the lateral area of the triangular prism:
Lateral area = perimeter of base * height
Lateral area = (9 + 12 + 13) * 5
Lateral area = 34 * 5
Lateral area = 170 cm^2
Now, calculate the total surface area of the triangular prism:
Surface Area = 2 * 22.5 + 170
Surface Area = 45 + 170
Surface Area = 215 cm^2
Therefore, 215 cm^2 of plastic wrap is needed to cover the wedge of cheese.
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 7 packages of stickers
you will need 414.14 cm^2 packages of stickers
you will need 5.5 packages of stickers
you will need 6 packages of stickers
To find the surface area of the triangular prism (wooden door stopper), follow a similar method as in the previous response:
Calculate the base area:
Base area = (1/2) * base * height
Base area = (1/2) * 8.9 * 5
Base area = 22.25 cm^2
Calculate the lateral area:
Lateral area = perimeter of base * height
Lateral area = (8.9 + 15.9 + 16.7) * 5
Lateral area = 41.5 * 5
Lateral area = 207.5 cm^2
Total surface area of the prism:
Surface Area = 2 * 22.25 + 207.5
Surface Area = 44.5 + 207.5
Surface Area = 252 cm^2
Given that one package of stickers covers 75 square centimeters, divide the total surface area of the door stopper by the coverage of one sticker package:
252 cm^2 / 75 cm^2 = 3.36
Since stickers can only be purchased in whole packs, round up the number to the next whole number:
You will need 4 packages of stickers to cover the wooden door stopper.
thats not right choose from one of the answers
From the given answer choices:
The closest answer to the surface area of the door stopper is:
- 5.5 packages of stickers
Therefore, you will need 6 packages of stickers to cover the wooden door stopper.