document.write( "Question 123463: May I please have some help finding the area?\r
\n" ); document.write( "\n" ); document.write( "Draw the parallelogram with vertices A(8, 5), B(17, 5), C(12, 10), and D(21, 10) on a coordinate plane. Find the area of the rectangle \n" ); document.write( "

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document.write( "Discussion
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document.write( "You wrote:
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document.write( "\"Draw the parallelogram with vertices A(8, 5), B(17, 5), C(12, 10), and
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document.write( "D(21, 10) on a coordinate plane. Find the area of the rectangle.\"\r
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document.write( "Here's the diagram:\r
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document.write( "Try as I might, I can't find a rectangle.  So I'll just assume you want the
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document.write( "area of the parallelogram.\r
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document.write( "The area of a parallelogram is given by  where b is the measure of
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document.write( "the base and h is the measure of the height.\r
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document.write( "Solution
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document.write( "Since the base of this parallelogram is parallel to the x-axis, the measure of
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document.write( "the base is calculated by the difference in the x-coordinates of the end
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document.write( "points of the base line segment.  \r
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document.write( "Note: You could use the distance formula to calculate the measure of the base,
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document.write( "but since the y-coordinates of the two points are equal, the distance formula
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document.write( "degenerates to the square root of the square of the difference in x, or simply
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document.write( "the difference in x.\r
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document.write( "Also, the height is parallel to the y-axis, so the measure of the height is
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document.write( "calculated by the difference in the y-coordinates of the end points of the
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document.write( "height line segment.  One of the end points is given and has a y-coordinate of
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document.write( "10.  But the other point is not given.  Fortunately, the missing end point
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document.write( "lies on the line segment representing the base.  Since that line segment is
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document.write( "parallel to the x-axis, all of the points on that line have the same
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document.write( "y-coordinate.  Therefore, the y-coordinate of the missing end point of the
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document.write( "height line segment is equal to the y-coordinate of either end point of the
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document.write( "base line segment, namely 5.  Hence, the measure of the height is \r
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document.write( "Now we have sufficient information to calculate the area of the parallelogram:\r
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document.write( " square units.\r
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document.write( "Check Answer
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document.write( "Cut off the triangle that was formed on the left of the parallelogram by the
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document.write( "construction of the height line segment.  Move this triangle to the left side
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document.write( "of the parallelogram to form a 9 unit by 5 unit rectangle.  Multiply 9 times 5
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document.write( "to get 45 which is the area of the rectangle equal to the area of the
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document.write( "parallelogram.  Alternatively, you could count the grid squares contained in
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document.write( "the rectangle to verify there are 45 of them.
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