## HourglassMage one year ago 2. A parallelogram has the vertices (-1, 2), (4, 4), (2, -1) and (-3, -3). Determine what type of parallelogram [10 points]. Find the perimeter and area [20 points].

1. HourglassMage

2. HourglassMage

That's what I got...but clearly it's not a parallelogram, so what am I doing wrong, and what do I need to do differently?

3. HourglassMage

4. ganeshie8
5. ganeshie8

^^thats how it should look. graphing is a very good idea, but u dont need to graph to solve this problem.

6. HourglassMage

Ohhh...duh. Apparently I'm going to be stupid today, brilliant. Thnx for the help! :)

7. ganeshie8

u figured how to work the problem ?

8. HourglassMage

BTW, someone told me the answer to this problem was 12. Are they right? I got 4.2... √((3) – (0))² + ((0) – (3))² = √3² + -3² = √9 + 9 = √18 ≈ 4.2

9. HourglassMage

yes, I did

10. ganeshie8

show me ur complete work

11. HourglassMage

For the first problem?

12. ganeshie8

for both

13. HourglassMage

Ah...ok

14. ganeshie8

what ever u have so far...

15. HourglassMage

just a mo, then

16. HourglassMage

17. HourglassMage

working on the second question now

18. ganeshie8

Are you given instructions that u need to work it by graphing ?

19. HourglassMage

Yeah, they taught graphing and the distance formula and whatnot

20. ganeshie8

no, i mean did the instructions specifically ask u to do this by graphing ?

21. ganeshie8

cuz, u should NOT use graphing unless the instructions say so

22. ganeshie8

the common/regular way to work this problem is by finding lengths of sides using distance formula and the slopes of sides using slope formula

23. HourglassMage
24. HourglassMage

Those were the directions they gave me

25. ganeshie8

cool :) then you're right ! they want u work it by graphing

26. HourglassMage

Given that they gave me the graph, I would assume that they want me to solve it by graphing, but I also used the distance formula to find the lengths of the sides

27. HourglassMage

ok :)

28. ganeshie8

good :) your length of sides, and perimeter are correct. but Area is wrong.

29. ganeshie8

squaring sides will not give u Area for a rhombus.

30. HourglassMage

ohh..just looked it up A - diagonal x diagonal/2

31. ganeshie8

Area of rhombus = $$\frac{1}{2} d_1 d_2$$

32. ganeshie8

yes^

33. HourglassMage

Great, now I have to find the diagonals, lol

34. ganeshie8

its easy from graph

35. ganeshie8

horizontal diagonal = 3--3 = 6 vertical diagonal = 3--3 = 6

36. ganeshie8

So, Area = $$\frac{1}{2} d_1 d_2 = \frac{1}{2} 6*6 = 18$$

37. ganeshie8

And that makes the given rhombus a SQUARE !

38. ganeshie8

so the given parallelogram is not just a rhombus, its also a SQUARE !

39. ganeshie8

for the type of parallelogram , you should say that its a square

40. ganeshie8

if that makes any sense..

41. HourglassMage

The parallelogram is a rhombus and a square?

42. ganeshie8

just say its a SQUARE !

43. HourglassMage

rhomus: all equal sides, two pairs of equal angles square: equal sides, equal angles

44. HourglassMage

oh, ok

45. HourglassMage

Does that change my equation for the area, then?

46. ganeshie8

all squares are parallelograms all squares are rhombuses all squares are rectangles all squares are quadrilaterals

47. ganeshie8

a square is many things

48. ganeshie8

yes it will change ur formula, but the answer will be same

49. HourglassMage

I see that, lol

50. ganeshie8

let me modify it and give u

51. HourglassMage

it will be?

52. HourglassMage

ok

53. ganeshie8

here is the corrected stuff for question 1 : http://prntscr.com/3euc4h

54. HourglassMage

55. HourglassMage

how do you find the diagonals inside a rhombus?

56. ganeshie8

use the distance formula

57. HourglassMage

oh, its the same process, ok, hold on

58. ganeshie8

ok, i presume u knw what a diagonal is :)

59. ganeshie8

it just connects the opposite vertices

60. ganeshie8

|dw:1398867292759:dw|

61. ganeshie8

|dw:1398867314860:dw|

62. ganeshie8

^^those two line segments joining opposite vertices are diagonals

63. HourglassMage

64. HourglassMage

Is that correct? I found it odd that I got the same area for #1 and #2...but maybe that's just a coincidence

65. ganeshie8

diagonals are not equal in rhombus

66. ganeshie8

so u need to calculate the 2nd diagonal also using distance formula

67. ganeshie8

and then use the area of rhombus formula : Area = $$\frac{1}{2}d_1 d_2$$

68. HourglassMage

69. HourglassMage

@ganeshie8

70. ganeshie8

looks good !

71. HourglassMage

thnx! :D