anonymous one year ago Describe a method you can use to find the area of the following shape. Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure.

1. anonymous

2. anonymous

@zepdrix

3. anonymous

@ganeshie8

4. zepdrix

Hey :) So umm.. how bout break it up into some more manageable shapes?

5. anonymous

okay, how should we start doing that?

6. zepdrix

|dw:1440473225733:dw|

7. anonymous

Are we wanting to divide it into 3 shapes or just however many we can make ?

8. zepdrix

Well I'm thinking like this maybe:|dw:1440473387371:dw|because rectangles and right triangles are really easy to deal with :)

9. zepdrix

Do you understand how to find the coordinates of each point?

10. zepdrix

Or rather I should say: Do you understand how to use the coordinates to find the side lengths?

11. anonymous

Okay(: So what is our first step? sorry im really not good at this. I think so isn't that do you count like up and down along y axis and and left to right on x axis ?

12. zepdrix

Provide specific details in your answer, including coordinates and descriptions of shapes used. Then, find the actual area of the figure. Yes, counting the squares is a much better way of doing it, but it looks like they want us to include coordinates and all of that business :(

13. anonymous

ughh :( okay so then how do we do that ?

14. zepdrix

|dw:1440473666198:dw|Do you understand how I came up with these two coordinates?

15. anonymous

For B you counted up 8 and counted left 11 units For C you counted left 11 units but the zero you didnt move at all ?

16. zepdrix

Yes, those distances. But your 'directions' seem backwards lol :) For B you count 8DOWN and 11RIGHT. We're starting from the point (0,0) and going towards B. I think you did it the other way around.

17. zepdrix

Oh boy this is gonna be tricky... I wonder if there is a simpler way we can chop this up...

18. anonymous

Oh your right i did my bad lol(: Hmmm could we do AC and that be a right triangle ? would that be an easier way to chop it up ?

19. zepdrix

|dw:1440474034288:dw|Hmm prolly not :) that leaves us with a nasty shape here

20. zepdrix

Are you comfortable with trapezoids?

21. zepdrix

|dw:1440474081780:dw|Cause maybe this would be easier

22. anonymous

kinda , im deffinetly gonna need help though

23. anonymous

So does that mean what we did with B and C earlier...forget that ?

24. zepdrix

It'll end up saving us some steps since we don't have to find all these little shapes in the middle. Just three now. To find the area of a trapezoid, we multiply the base length by the average of the side/height lengths.$\large\rm A=b\cdot\frac{h_1+h_2}{2}$ How long is side BC?

25. anonymous

I thought 11 units , correct?

26. zepdrix

|dw:1440474292576:dw|I'm just gonna label all of the points that we'll need.

27. zepdrix

|dw:1440474388966:dw|

28. zepdrix

from 0 down to -8

29. anonymous

so would the height be -8 and 0 for BC

30. zepdrix

The height is the distance from 0 to -8. That ends up being a distance of 8 if you count the boxes, ya?

31. anonymous

Yes your right, im just trying to plug in the h1 and h2 too quick lol sorry

32. zepdrix

|dw:1440474556848:dw|How bout from D down the bottom? You're at -3 and you're going down to -8, how many boxes between those?

33. zepdrix

Make sure you're using the original image :) Mine kinda stinks since you can't count the boxes lol

34. anonymous

Okay(: Would that be 5?

35. zepdrix

|dw:1440474733035:dw|Good :O Then the base? Looks like we're going from x=6 over to x=11

36. anonymous

would the base be 6?

37. zepdrix

We're going from 6 to 11. You can do subtraction if you feel more comfortable with that. 11-6 = 5 So a length of 5 across the bottom.

38. anonymous

Okay i must have counted wrong, so now i plug in the numbers?

39. zepdrix

$\large\rm A=b\cdot\frac{h_1+h_2}{2}\qquad\to\qquad A_1=5\cdot\frac{5+8}{2}$Plug all the information in! :) What do we get for the area of our first shape? Yah sorry I stole some of the fun there, just trying to move this along hehe.

40. anonymous

Haha its okay(: so then it would be 13/2 = 6.5 then 6.5 X5 = 32.5 SO would our answer be 32.5?

41. zepdrix

|dw:1440475130927:dw|Ok great! We're 1/3 done lol

42. anonymous

Great(: ! So now do we do the same thing to the other shape ?

43. zepdrix

Let's ignore the coordinates for now. Just use those in your explanation maybe :p|dw:1440475216912:dw|

44. zepdrix

Yes, let's work on this trapezoid in the bottom left here. Can you figure out the side lengths by counting the boxes?

45. anonymous

That would be 2 if your counting up and if your counting left then that would be 5

46. zepdrix

Hmm 5 doesn't sound quite right.

47. anonymous

Then im confused i counted to the F and it was 5 units

48. zepdrix

|dw:1440475453452:dw|

49. anonymous

Oh i see my mistake, i moissed one, my bad :/

50. zepdrix

So we have our information again, good. $$\large\rm h_1=1,\quad h_2=6,\quad b=2$$ plug it in to find the area of your second shape.

51. anonymous

One question first, how did you get the 1?

52. anonymous

A = 7?

53. zepdrix

|dw:1440475703801:dw|

54. zepdrix

So that length is 1 from 5 to 6, ya? :o

55. anonymous

Oh yeah your right , duhhh(: so my answer would be 7 correct ?

56. zepdrix

|dw:1440475843531:dw|Mmmmmm k good. let's try to figure out this last one. Luckily we have a free side already! Since this trapezoid shares a side with the bottom one, we know that the long edge is still 6.

57. zepdrix

What about the other lengths? :o

58. anonymous

well from D to E that would be 2

59. anonymous

the other length would be 3

60. zepdrix

|dw:1440476101788:dw|Ok good! :)

61. anonymous

h1 = 3 h2 = 6 b=2?

62. zepdrix

The h's should be across from one another.

63. anonymous

b= 3 and h2= 2

64. anonymous

Im sorry , for the confusion im just trying to understand .. so the answer would be 12?

65. zepdrix

|dw:1440476358788:dw|Good. And the total area would be the sum of those three areas. $$\large\rm A=A_1+A_2+A_3$$