## jacobciezki one year ago What is the area of the figure?

1. jacobciezki

one sec

2. jacobciezki
3. jacobciezki

there

4. SolomonZelman

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5. SolomonZelman

|dw:1436297153477:dw|

6. SolomonZelman

what is this length that I marked with a question mark? how long is it, do you know?

7. jacobciezki

idk the whole line is 17

8. SolomonZelman

yes, and you know that up to that point the length is 12

9. SolomonZelman

so the little segment that I marked is how long?

10. jacobciezki

um 5

11. SolomonZelman

yes, exactly:)

12. SolomonZelman

Now I will re-write the picture.

13. jacobciezki

ok

14. jacobciezki

soo

15. SolomonZelman

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16. SolomonZelman

that is all you need to know, and now we will split this shape into two different shapes. - triangle - trapezoid

17. SolomonZelman

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18. jacobciezki

how you do that

19. SolomonZelman

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20. SolomonZelman

Can you find the area of this triangle here?

21. jacobciezki

umm 360

22. SolomonZelman

When finding the area of a triangle, we apply the following formula. $$\large \displaystyle {\rm Area}=\frac{({\rm base})\times({\rm height}) }{2}$$ (you were almost correct)

23. jacobciezki

180

24. SolomonZelman

yes

25. SolomonZelman

So the area of the triangle is 180.

26. SolomonZelman

Now the trapezoid.

27. SolomonZelman

Whenever we have a trapezoid with bases $${\rm B}_1$$ and $${\rm B}_2$$, and a hieght $${\rm H}$$, we apply this formula: (below) $$\displaystyle \large {\rm Area}=\left(\frac{{\rm B}_1~+~{\rm B}_2}{2}\right)\times {\rm H}$$

28. SolomonZelman

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29. SolomonZelman

So your bases are 14 and 18 (doesn't matter which one you assign $${\rm B}_1$$ and which you assign $${\rm B}_2$$). And your height is 5. ---------------------------------------------------- $${\rm B}_1$$ and $${\rm B}_2$$ $$\huge \rightarrow$$ $$14$$ and $$18$$ $${\rm H}=5$$ ---------------------------------------------------- Now plug in this into the formula (below). $$\displaystyle \large {\rm Area}=\left(\frac{{\rm B}_1~+~{\rm B}_2}{2}\right)\times {\rm H}$$

30. jacobciezki

80 ?????????????????//

31. jacobciezki

what is it 180 188 or 80

32. SolomonZelman

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33. SolomonZelman

So the area of the trapezoid is 80 (and recall that the area of the triangle is 180)

34. SolomonZelman

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35. SolomonZelman

so then if triangle is 180 and trapezoid is 80, the entire figure has an area of?

36. jacobciezki

260

37. wil476003

The triangle would not be 180 it is 108 becuase 9 times 12 equals 108 and then you divide it by two to get 54 and then you multiply it by 2 so the full answer would be 188

38. jacobciezki

SolomonZelman

39. SolomonZelman

yes I allowed an error by a triangle

40. SolomonZelman

tnx for correcting me @wil476003 the height of the triangle is 12. So, Area (of the triangle) = (12 • 18) ÷ 2 = 108

41. SolomonZelman

I apologize for my mistake, and for my departures. I am cooking for my family (or at least trying to), and for this reason I had to leave for undefined periods of time.

42. SolomonZelman

see why triangle has an area of 108?

43. jacobciezki

yea

44. SolomonZelman

Then the entire shape = triangle + trapezoid = 108 + 80 = 188 (as wil476003 previously asserted)

45. SolomonZelman

gtg again

46. SolomonZelman

sory, bye