Check all that apply
she did not find the correct vertex; it should be at (8, 5).
she used the wrong area formula; it should be a=1/2 b * h.
she used the wrong length for the base; it should be 7, like the given base.
she used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3.
she should have found a segment for the top that was not parallel to the bottom.

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the given base

# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3

Step-by-step explanation:

* Lets explain how to solve the problem

- She has three vertices of the parallelogram

- The vertices are (12 , 2) , (5 , 2) , (1 , 5)

∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates

∴ The length of the base of the parallelogram is 12 - 5 = 7 units

- In parallelogram each two opposite sides are equal and parallel

∴ The opposite side to the base is 7

∴ The x coordinate of the missing point equal the x-coordinate of the

  point (1 , 5) + the length of the base

∴ The x coordinate of the missing vertex  = 1 + 7 = 8

∵ The y-coordinate of the missing vertex is the same with the

   y-coordinate of the point (1 , 5)

∴ The y-coordinate of the missing vertex is 5

∴ The missing vertex is (8 , 5)

- The area of the parallelogram is A = bh, where b is the base of it

  and h is the height of this base

- Remember the height must be perpendicular on the base

∵ The perpendicular distance between the two parallel bases is the

  difference between the y-coordinates of the two points each one

  belong to one of the two parallel bases

∴ The height of the parallelogram = 5 - 2 = 3 units

∴ Its area = 7 + 3 = 21 units ²

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the

   given base

# She used a side length of the parallelogram for the height instead

  of a line segment perpendicular to the base; the height should be 3