## Kailee1423 one year ago Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.

1. Kailee1423

@phi I would know how to do this if it wasn't for the slant height. How do I make it a regular height?

2. phi

|dw:1441659885410:dw|

3. phi

|dw:1441659931267:dw|

4. phi

not my best drawing. but the idea is the height from the top to the base lands exactly in the center of the square. the distance to a side is 1/2 the distance across, so 5

5. phi

if we concentrate on the triangle |dw:1441660064080:dw|

6. Kailee1423

So 5 squared + 13 squared = h squared? That would be 194 = h squared. DO I dived 194 by 2 now?

7. Kailee1423

divide*

8. phi

in $a^2 + b^2 = c^2$ c is *always* the hypotenuse (the longest side) in this problem, the 13 is the hypotenuse

9. Kailee1423

Oh ok. I should've known that. Lol. So h squared + 5 squared = 13 squared. (I don't know how to put the equation on here)

10. phi

you could type h^2 +5^2 = 13^2 5^2 means 5*5 13^2 means 13*13

11. Kailee1423

Ok. Thanks! Lol and then once you solve that you do it exactly like the last problem we did?

12. phi

yes. what do you get for h^2 ?

13. Kailee1423

h^2+5^2=13^2 h^2=13^2-5^2 h^2=144 144/2=72 Did I do that right?

14. phi

h^2=144 ok. now take the square root of both sides. (h^2/2 does not "undo" the square)

15. phi

the idea is $$\sqrt{h^2 } =h$$ so we do that to both sides

16. Kailee1423

I did the sqare root of 144 on my calcalator and I got 12.

17. phi

yes, h=12 as a check you can do 5^2 + 12^2 and it should give 13^2 (and it does)

18. phi

btw, (some) people memorize 3,4,5 as forming a right triangle (5 is the hypotenuse) and also 5,12,13 is a right triangle. there are lots more, but these two show up on tests a lot.

19. Kailee1423

Ok I have one more question to post. I hope I'm not bothering you!

20. phi

what did you get for the volume. (it would be a shape to make a mistake now)

21. Kailee1423

1200?

22. phi

what is the formula for the volume of a pyramid?

23. Kailee1423

1/3BH

24. phi

put in numbers for B and h

25. Kailee1423

Oh it's 400. I forgot to put the 1/3 when I first did it

26. phi

yes, 400

27. Kailee1423

That would have been a simple mistake lol Thanks