SOLUTION: determine the area and perimeter of the polygon having the following for vertices. (2,4)(6,1)(14,16)(7,16)
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Question 643317: determine the area and perimeter of the polygon having the following for vertices. (2,4)(6,1)(14,16)(7,16)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Perimeter: Apply the distance formula four times to get the measures of each of the sides then add them.
Distance formula:
^2\ +\ (y_1\ -\ y_2)^2})
where )
and )
are the coordinates of the given points.
Area: Construct either diagonal and use the distance formula to calculate the measure of that diagonal. Constructing the diagonal creates two triangles for which you now know the measures of all three sides. Using that information in Heron's Formula, you can calculate the area of each of the triangles. The sum of the two triangle areas is the area of the quadrilateral.
Heron's Formula:
(s\ -\ b)(s\ -\ c))
Where 
, 
, and 
are the measures of the three sides and 
is the semi-perimeter defined as the perimeter divided by 2, to wit: 
John
My calculator said it, I believe it, that settles it
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