PLZ HELP WILL MEDAL AND FAN What is the surface area of the triangular prism shown with height 5 feet? You can use the formula: SA = 2B + PH.

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PLZ HELP WILL MEDAL AND FAN What is the surface area of the triangular prism shown with height 5 feet? You can use the formula: SA = 2B + PH.

Mathematics
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eight hundred eighty square feet nine hundred ten square feet one thousand two hundred square feet two thousand five hundred fifty square feet

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Do you understand the given formula for the total surface area of the prism?
not that much
Ok. I'll explain the formula to you then you can use the formula. A prism is a solid that is created by taking a polygon, the base, and sliding the base a certain distance.
In your case you have a triangular prism. The bases are triangles.
Here is one base of your prism. This base now slides 5 ft toward the back of the drawing. |dw:1437328868066:dw|
|dw:1437328935002:dw|
There is the prism. The bases can be any polygon. In your case, the bases are triangles. The side faces of a prism are always parallelograms.
If the prism is a right prism, like your is, then the side faces are not only parallelograms, but they are rectangles.
Now let's look at the surface area formula. SA = 2B + PH The total surface are of a prism is the sum of two components, the area of the bases and the area of the lateral faces. 2B means two times B, the area of the base. Find the area of a base, and multiply by 2 to account for the are of the two bases. PH means the perimeter of the base times the height. This gives you the lateral area. This is the area of all the rectangular faces combined.
Now we can work on the two components of the area and find the total surface area.
Base area: 2B Each base is a triangle. Looking in the figure, each base is a triangle with base 30 ft and height 16 ft. How do you find the area of a triangle with base 30 ft and height 16 ft?
multiply
and divide by 2
\(\Large A_{triangle} = \dfrac{bh}{2} \)
so i need to do 30x16/2?
Multiply the base by the height and divide by 2. That is the area of each base. What do you get?
Yes, exactly. Do that.
240 that is what i got
Correct. That is B, the area of each base. The formula has 2B, the area of both bases, so multiply 240 ft^2 by 2 to find 2B.
so would that be 480
Correct. The 2B part is 480 ft^2. Now we need to work on the lateral surface area, the surface area of the three rectangular sides.
How do I find out PH?
The lateral surface area is PH. P is the perimeter of the base. H is the height of the prism. Looking at the figure, we see the base is a triangle with side lengths 30 ft, 16 ft, and 34 ft. Can you find P, the perimeter of the triangular base?
80
Correct. Now look in the figure again. What is the height of the prism?
16
No. Be careful. I know it can be confusing. We have two different sides called height here. The height of the base is 16 ft. We also have the height of the prism. In this case we need the height of the prism, not the height of the base.
so it would be 5?
|dw:1437330179269:dw|
|dw:1437330207419:dw|
Correct. 5 ft is the height of the prism.
Now you need to find PH. Multiply the perimeter of the base by the height of the prism. What is 80 ft * 5 ft ?
450
*400
Really? What is 8 * 5?
Oh. I see. Great 400 ft^2.
Now we finish by adding the two components of the area. SA = 2B + PH SA = 480 ft^2 + 400 ft^2
so now I do 400+480=880, is that my answer
Here is how the problem can be shown: \(SA = 2B + PH\) \(SA = 2 \times \dfrac{bh}{2} + (30 ~ft + 16 ~ft + 34 ~ft)(5 ~ft) \) \(SA = 2 \times \dfrac{(30 ~ft)(16~ft)}{2} + (80~ft)(5~ft) \) \(SA = 2 \times 240~ft^2 + 400~ft^2\) \(SA = 480 ~ft^2 + 400~ft^2\) \(SA = 880 ~ft^2\)
Yes, 880 ft^2 is the answer.
Thank you so much, you just didn't help me find the answer but you also helped me understand
You are very welcome. I'm glad you understand it now.

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