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Question 1199552: I've been trying to use the same formula that I use to find the area of a triangle but it is not giving me the correct answer.
Find the area of the parallelogram with the following vertices:
11. (-2, 3), (5, 8), (3, 3), and (0, 8)
A. 16 sq units
B. 20 sq units
C. 34 sq units
D. 18 sq units
E. 25 sq units
F. 36 sq units
12. (-2, 7), (-4, 4), (-11, 4), and (-9, 7)
A. 15 sq units
B. 63 sq units
C. 28 sq units
D. 21 sq units
E. 36 sq units
F. 14 sq units
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the area of the parallelogram with the following vertices:
11. A(-2,3), B(5,8), C(3,3), and D(0,8)
A D B C A
-2 0 5 3 -2
3 8 8 3 3
Add the diagonal products starting upper left
-2*8 + 0*8 + 5*3 + 3*3 = -16+15+9 = 8
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Add the diagonal products starting lower left
3*0 + 8*5 + 8*3 + 3*-2 = 0+40+24-6 = 58
The difference is 50.
The area is 1/2 that, = 25 sq units.
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This works for all convex polygons, but the points have to be in order around the perimeter. Notice it's A, D, B, C
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12. A(-2,7), B(-4,4), C(-11,4), and D(-9,7)
A. 15 sq units
B. 63 sq units
C. 28 sq units
D. 21 sq units
E. 36 sq units
F. 14 sq units
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Part (a)
If you draw the given points in a coordinate plane, you will see
(even with unarmed eye) that one pair of sides is horizontal (y = 3 and y = 8) of the length of 5 units,
while the height of the parallelogram (the distance between its parallel horizontal sides) is 8 - 3 = 5 units.
It gives the area 5*5 = 25 square units.
In part (b), the same reasoning does work, allowing you to get the answer MENTALLY.
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At the beginning of your post you write
" I've been trying to use the same formula that I use to find
the area of a triangle but it is not giving me the correct answer. "
It is not surprising, because you have no any reason to use
" the same " formula for totally different problem.
It is like jumping off a tower upside down into a swimming pool with no water.
In opposite, it would be surprising if this formula would work.
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