anonymous one year ago Find the surface area of a pyramid if its height is 4 cm and its base is a rectangle with side lengths 4 cm and 6 cm. Round to the nearest whole number.

1. jim_thompson5910

What is the area of the base?

2. anonymous

24 cm^2

3. jim_thompson5910

correct

4. jim_thompson5910

|dw:1435548018859:dw|

5. jim_thompson5910

|dw:1435548042782:dw|

6. jim_thompson5910

|dw:1435548055051:dw|

7. jim_thompson5910

do you see how I got that triangle I just added?

8. anonymous

yes

9. jim_thompson5910

it's a right triangle with legs 3 and 4 the hypotenuse is what?

10. anonymous

5

11. jim_thompson5910

|dw:1435548291256:dw|

12. jim_thompson5910

we will have 2 triangles on the lateral face of the pyramid that look like this |dw:1435548321950:dw| base = 4 height = 5

13. jim_thompson5910

what is the area of that triangle?

14. anonymous

10cm^2

15. jim_thompson5910

there are 2 of these triangles, so they add to 10+10 = 20 cm^2 the front and back faces |dw:1435548418230:dw|

16. jim_thompson5910

|dw:1435548440907:dw|

17. jim_thompson5910

|dw:1435548484189:dw|

18. anonymous

So for the other 2 sides would the area be 15cm^2.

19. anonymous

15+15=30cm^2

20. jim_thompson5910

how are you getting 15?

21. anonymous

And the bottom area would be 6x4=24cm^2

22. anonymous

I got 15 from multiplying 6x5=30/2=15cm^2. Would that not be correct?

23. jim_thompson5910

that other hypotenuse isn't 5

24. jim_thompson5910

|dw:1435548754459:dw|

25. anonymous

4.47

26. jim_thompson5910

so you have 2 more triangles, each looking like this |dw:1435548837682:dw|

27. anonymous

Would i make 4.47 into 4 because the problem says to round the nearest whole number.

28. jim_thompson5910

round when you're done calculating

29. jim_thompson5910

so it might be better to use more decimal digits instead of 4.47 maybe use 4.47213595 or something $\Large \sqrt{20} \approx 4.47213595$

30. anonymous

Area=13.416407

31. jim_thompson5910

that's the area of one triangle there are 2 of them

32. anonymous

26.832814cm^2

33. jim_thompson5910

Summary: you have a base that's 24 cm^2 the front and back triangles have a total area of 20cm^2 the left and right triangles have a total area of 26.832814 cm^2

34. anonymous

The answer would be then 70.83 or 71cm^2 (the answer was in my book but i couldn't see what i was doing wrong THANK YOU SO MUCH :D)

35. jim_thompson5910

you're welcome