## anonymous one year ago 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.

1. anonymous
2. anonymous

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

3. anonymous

@paki

4. mathstudent55

Do you understand the given formula for the total surface area of the prism?

5. anonymous

not that much

6. mathstudent55

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.

7. mathstudent55

In your case you have a triangular prism. The bases are triangles.

8. mathstudent55

Here is one base of your prism. This base now slides 5 ft toward the back of the drawing. |dw:1437328868066:dw|

9. mathstudent55

|dw:1437328935002:dw|

10. mathstudent55

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.

11. mathstudent55

If the prism is a right prism, like your is, then the side faces are not only parallelograms, but they are rectangles.

12. mathstudent55

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.

13. mathstudent55

Now we can work on the two components of the area and find the total surface area.

14. mathstudent55

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?

15. anonymous

multiply

16. mathstudent55

and divide by 2

17. mathstudent55

$$\Large A_{triangle} = \dfrac{bh}{2}$$

18. anonymous

so i need to do 30x16/2?

19. mathstudent55

Multiply the base by the height and divide by 2. That is the area of each base. What do you get?

20. mathstudent55

Yes, exactly. Do that.

21. anonymous

240 that is what i got

22. mathstudent55

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.

23. anonymous

so would that be 480

24. anonymous

@mathstudent55

25. mathstudent55

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.

26. anonymous

How do I find out PH?

27. mathstudent55

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?

28. anonymous

80

29. mathstudent55

Correct. Now look in the figure again. What is the height of the prism?

30. anonymous

16

31. mathstudent55

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.

32. anonymous

so it would be 5?

33. mathstudent55

|dw:1437330179269:dw|

34. mathstudent55

|dw:1437330207419:dw|

35. mathstudent55

Correct. 5 ft is the height of the prism.

36. mathstudent55

Now you need to find PH. Multiply the perimeter of the base by the height of the prism. What is 80 ft * 5 ft ?

37. anonymous

450

38. anonymous

*400

39. mathstudent55

Really? What is 8 * 5?

40. mathstudent55

Oh. I see. Great 400 ft^2.

41. mathstudent55

Now we finish by adding the two components of the area. SA = 2B + PH SA = 480 ft^2 + 400 ft^2

42. anonymous

so now I do 400+480=880, is that my answer

43. mathstudent55

Here is how the problem can be shown: $$SA = 2B + PH$$ $$SA = 2 \times \dfrac{bh}{2} + (30 ~ft + 16 ~ft + 34 ~ft)(5 ~ft)$$ $$SA = 2 \times \dfrac{(30 ~ft)(16~ft)}{2} + (80~ft)(5~ft)$$ $$SA = 2 \times 240~ft^2 + 400~ft^2$$ $$SA = 480 ~ft^2 + 400~ft^2$$ $$SA = 880 ~ft^2$$

44. mathstudent55

Yes, 880 ft^2 is the answer.

45. anonymous

Thank you so much, you just didn't help me find the answer but you also helped me understand

46. mathstudent55

You are very welcome. I'm glad you understand it now.

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