Triangluar prism dimensions:
5 cm in height
S1=15.9 cm
S2=16.7 cm
S3= 5 cm
Length is 8.9 cm
Find the surface area of the triangular prism
Surface area of a triangular prism is calculated using the formula:
Surface Area = 2*(base area) + (perimeter of base)*(height) + (2*side area)
First, we need to calculate the base area:
Base area = 1/2 * base * height = 1/2 * 15.9 * 5 = 39.75 cm^2
Next, we need to calculate the perimeter of the base:
Perimeter = S1 + S2 + S3 = 15.9 + 16.7 + 5 = 37.6 cm
Now, we can calculate the side area:
Side area = length * height = 8.9 * 5 = 44.5 cm^2
Now we can plug in the values and calculate the total surface area:
Surface Area = 2*(39.75) + (37.6)*(5) + (2*44.5) = 79.5 + 188 + 89 = 356.5 cm^2
Therefore, the surface area of the triangular prism is 356.5 cm^2.
No. Use this formula: BH+(S1+S2+S3)L
Sure, let's use the formula you provided to calculate the surface area of the triangular prism:
Surface Area = BH + (S1 + S2 + S3) * L
Surface Area = 39.75 + (15.9 + 16.7 + 5) * 8.9
Surface Area = 39.75 + 37.6 * 8.9
Surface Area = 39.75 + 334.64
Surface Area = 374.39 cm^2
Therefore, the surface area of the triangular prism using the formula BH + (S1 + S2 + S3) * L is 374.39 cm^2.
Use that surface area to solve the question:
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.)
Answer choices: 6 packs of stickers
7 packs of stickers
To cover the surface area of the door stopper, we need to determine how many packages of stickers are needed.
The surface area of the door stopper is 374.39 cm^2, and each package of stickers covers a surface area of 75 cm^2.
Number of packages needed = Surface area of door stopper / Surface area covered by one package
Number of packages needed = 374.39 cm^2 / 75 cm^2 ≈ 4.99
Since we can only purchase whole packs of stickers, we need to round up to the nearest whole number. Therefore, the closest number to the surface area of the door stopper in terms of packages of stickers needed is 5 packs of stickers.
So, the correct answer choice would be neither of the provided options.
The answer said the closest
If we are looking for the closest answer choice, we need to see which of the given choices, 6 packs of stickers or 7 packs of stickers, is closer to the actual number of sticker packs needed to cover the surface area of the door stopper.
We calculated that we need approximately 4.99 packs of stickers to cover the surface area of the door stopper. Since we can only purchase whole packs of stickers, the closest whole number to 4.99 is 5 packs of stickers.
Therefore, the closest answer choice provided would be 6 packs of stickers, as it is closer to the actual number of sticker packs needed compared to 7 packs.