Parallelogram area

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doeordie

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12. Consider a parallelogram with perimeter 36. What is its area?

1) One side is twice as long as one other
2) One angle is 80 degrees

  • A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • D. EACH statement ALONE is sufficient.
  • E. Statements (1) and (2) TOGETHER are NOT sufficient.
Why would the answer be C? Area of parallelogram = base * height; the perimeter and the first statement should be enough to find the base and the height.

The solution even says that the base*height is one way of solving for the area. The solution says there's another way involving angles, but why would this make neither statement sufficient? The first statement is sufficient, the second is not.

What am I missing??

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12. Consider a parallelogram with perimeter 36. What is its area?

1) One side is twice as long as one other
2) One angle is 80 degrees

  • A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • D. EACH statement ALONE is sufficient.
  • E. Statements (1) and (2) TOGETHER are NOT sufficient.
Why would the answer be C? Area of parallelogram = base * height; the perimeter and the first statement should be enough to find the base and the height.

The solution even says that the base*height is one way of solving for the area. The solution says there's another way involving angles, but why would this make neither statement sufficient? The first statement is sufficient, the second is not.

What am I missing??
The correct answer is C
Statement 1 alone will be sufficient if it were a rectangle which is not the case here.
From statement 1 you can solve for both sides.
2L +2W = 36 ( given)
From statement 1 we get:
2(2W) +2W = 36
You get W = 6 and L = 12
This is not enough to find the area of the parallelogram.
From statement 2 if you know one of the angles is 80 you can find the height using trig and then you can find the area.
A = base x height
The base is 12 and the height can be found using trig:
Sin (80) = H/6
Remember you don't have to actually find the area, just decide if you have enough information to solve the problem.
See the attached picture.View attachment 218159 View attachment 218159 View attachment 218159
 

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Area = Side length × Base length x Sin(80)
Area = 6×12×Sin(80)
Area = 70.9 square units

We were given the side length and base length by the perimeter of 36 and also an angle.

In addition, the formula Area = Base × Height given in the explanation can also be used to find the area of a parallelogram, square, or rectangle. However, the height was not given and should not be confused with a side length.
 
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