## Sunshine447 3 years ago The figure below shows two similar right triangular prisms. What is the volume of Prism B rounded to the nearest hundredth cubic unit?

1. Sunshine447

@phi

2. Sunshine447

@Agent_Sniffles @amistre64 @jim_thompson5910 @Hero

3. phi

two similar right triangular prisms. SIMILAR means that the ratio of their sides are the same number for example, look at the shortest side of the big prism and divide it by the length of the shortest side in the smaller prism what do you get?

4. Sunshine447

.56

5. Sunshine447

or 1.8... idk which

6. phi

I meant 9/6 = 3/2 or 1.5 now look at the other leg: the longer side of the big prism is 10.5 divide this by the corresponding side of the other prism what do you get?

7. Sunshine447

ohhh okay

8. Sunshine447

1.5

9. phi

now what do you think the (unknown) height (call it h) divided by 5 is ? h/5 = 1.5 (the same ratio) now find h

10. Sunshine447

7.5?

11. phi

yes. why the ? Is your calculator broken? But now you can find the volume of the big prism volume of Prism B is the area of its base (it's a triangle) times its height (just found to be 7.5) can you find the area of the base? then multiply by the height 7.5 to get the volume

12. Sunshine447

how do i find the area of the base?

13. phi

didn't you just do the area of a triangle in the last question?

14. Sunshine447

is it b*h/2? My lesson isn't very clear on what's what....

15. phi

yes base times height divided by 2 base is one of the legs, the height (or altitude) is the line perpendicular to the base . The height makes a 90 angle with the base. In your picture, that little square in the corner of the 2 legs means 90 deg so your base and height are the 2 legs in the triangle.

16. Sunshine447

the base is 47.25 then. Right?

17. phi

Examples |dw:1349210955962:dw|

18. phi

base is 47.25 then. Right? I would say area of the base (of the prism) (there is also the base of the triangle, which is just 1 leg) Area of the base is 0.5*9*10.5= 47.25 now find the volume by multiplying that by the height of the prism

19. Sunshine447

didnt you just do that?

20. Sunshine447

or do i multiply 47.35*9?

21. Sunshine447

*47.25 sry typo

22. phi

don't lose track of what we are doing 1) we found the h using the idea of similar figures. h= 7.5 2) we found the area of the base of the prism A= 47.25 3) we find the volume by multiplying A*h

23. Sunshine447

354.375

24. Sunshine447

or 354.38 if we round up

25. phi

This question took a few steps, and you need to know a few facts...

26. Sunshine447

ok