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What is the area of parallelogram ABCD? 1. AB = BC = CD = DA [#permalink]
 29 Oct 2007, 08:34
What is the area of parallelogram ABCD?
1. AB = BC = CD = DA = 1
2. AC = BD = sqrt(2)
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Manager
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1) SUFF
the parallelogram is a square
2) SUFF
using pythagorean theory we can see that the sides must be equal to 1, with hypotenuse of sqrt(2).
D.
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(C) for me 
Stat1
We have a rhombus...
INSUFF.
Stat2
We have a rectangle...
INSUFF.
Both 1 and 2
We are sure to have a square.
SUFF.
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Manager
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Got it --
1) So even though you know the sides, this is not sufficient to solve for base & height of the rhombus.
INSUFF
2) Rectangle, not rhombus here.
Both:
Rectangle with equal sides = square with sides 1
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bmwhype2 wrote: What is the area of parallelogram ABCD?
1. AB = BC = CD = DA = 1
2. AC = BD = sqrt(2)
1 alone could yield either a square or a rhombus.
2 alone tells nothing except that the diagonal is root 2.
1 and 2 combined give us an idea that it's a square indeed.
So C.
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Manager
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In 2), would it be possible to use pythagoream theorem here to solve for the sides?
A^2 + B^2 = C^2 where c = sqrt(2)
so A^2 + B^2 = 2, so the sides must be 1 & 1, no?
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yuefei wrote: In 2), would it be possible to use pythagoream theorem here to solve for the sides?
A^2 + B^2 = C^2 where c = sqrt(2)
so A^2 + B^2 = 2, so the sides must be 1 & 1, no?
Again you are assuming that the sides are at right angles (viz the figure is a rectangle/square) for the pythagorean theorem to be applicable.
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Got it... the parallelogram with congruent diagnols could be a trapezoid, thus the angles are not 90. Thanks
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For 2, to me, parallelogram ABCD + equal sizes of diagonal = rectangle
As a parallelogram ABCD implies that diagonales crosses one another at their middle points, the equal sizes of diagonal assure us that we have a square... not matter the angle between diagonale
A trapezoid cannot be a parallelogram
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CEO
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Fig wrote: For 2, to me, parallelogram ABCD + equal sizes of diagonal = rectangle As a parallelogram ABCD implies that diagonales crosses one another at their middle points, the equal sizes of diagonal assure us that we have a square... not matter the angle between diagonale A trapezoid cannot be a parallelogram Are the diagonals in a rhombus equal?
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bmwhype2 wrote: Fig wrote: For 2, to me, parallelogram ABCD + equal sizes of diagonal = rectangle As a parallelogram ABCD implies that diagonales crosses one another at their middle points, the equal sizes of diagonal assure us that we have a square... not matter the angle between diagonale A trapezoid cannot be a parallelogram Are the diagonals in a rhombus equal? Not necessary...
If so, it's also a square
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CEO
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Fig wrote: bmwhype2 wrote: Fig wrote: For 2, to me, parallelogram ABCD + equal sizes of diagonal = rectangle As a parallelogram ABCD implies that diagonales crosses one another at their middle points, the equal sizes of diagonal assure us that we have a square... not matter the angle between diagonale A trapezoid cannot be a parallelogram Are the diagonals in a rhombus equal? Not necessary... If so, it's also a square thanks
A square is a rhombus and a rectangle. In other words, if each angle of a rhombus is 90° then it's a square.
1. AB = BC = CD = DA = 1
all sides equal, can be a rhombus or square.
Area of a square = s^2
Area of a rhombus = s*h
diff formulas, INSUFF
2. AC = BD = sqrt(2)
diagonals are equivalent. must be a square.
Area of a square = s^2
sides not defined
INSUFF
taken together, we see it is a s:s:sqrt(2) right triangle
area= 1^2=1
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bmw -- you stated the following in 2)
"diagonals are equivalent. must be a square.
Area of a square = s^2
sides not defined"
Can't you solve for s?
Create a triangle with hypotenuse sqrt(2) and side s.
s^2 + s^2 = sqrt(2)
s^2 = sqrt(2)/2
Is this possible?
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bmwhype2 wrote: Fig wrote: bmwhype2 wrote: Fig wrote: For 2, to me, parallelogram ABCD + equal sizes of diagonal = rectangle As a parallelogram ABCD implies that diagonales crosses one another at their middle points, the equal sizes of diagonal assure us that we have a square... not matter the angle between diagonale A trapezoid cannot be a parallelogram Are the diagonals in a rhombus equal? Not necessary... If so, it's also a square thanks A square is a rhombus and a rectangle. In other words, if each angle of a rhombus is 90° then it's a square. 1. AB = BC = CD = DA = 1 all sides equal, can be a rhombus or square. Area of a square = s^2 Area of a rhombus = s*h diff formulas, INSUFF 2. AC = BD = sqrt(2) diagonals are equivalent. must be a square. Area of a square = s^2 sides not defined INSUFF taken together, we see it is a s:s:sqrt(2) right triangle area= 1^2=1 Well, one right angle is enough  ... As a rhombhus is a paralelogram, 1 right angle creates 1 right angle by a parallel construction then the 2 last ones by another parallel construction
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CEO
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Here is a similar question
Points A, B, C and D form a quadrilateral. Is AC longer than BD?
1. angle ABC > angle BCD
2. AB = BC = CD = DA
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CEO
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yuefei wrote: bmw -- you stated the following in 2)
"diagonals are equivalent. must be a square.
Area of a square = s^2
sides not defined"
Can't you solve for s?
Create a triangle with hypotenuse sqrt(2) and side s.
s^2 + s^2 = sqrt(2)
s^2 = sqrt(2)/2
Is this possible?
you dont know that the sides are equal. it can yield a rectangle.
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