SOLUTION: Determine the area of the quadrilateral whose vertices are (1,3), (6,5), (9,1) and
(3,-3).
Algebra.Com
Question 245876: Determine the area of the quadrilateral whose vertices are (1,3), (6,5), (9,1) and
(3,-3).
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Perhaps this is a rather unorthodox way of approaching this problem, but it is the only way I see where the arithmetic remains simple throughout.
First plot your points and draw the quadrilateral. Then construct the two vertical lines:
and
Next, construct the two horizontal lines:
and
Note that the intersections of the two horizontal and two vertical lines are the points:
,\,(9,5),\,(9,-3),\,(1,-3))
The fact that these are horizontal and vertical lines should make the measurement calculations a simple mental exercise -- the four newly defined points form an 8 by 8 square, hence a square with an area of 64 square units.
The triangle formed by points:
,\,(1,3),\,(6,5))
Can easily be seen to be a right triangle with a short leg that measures 2 and a long leg that measures 5. Hence, the area of this triangle is 5 times 2 divided by 2 is 5.
In a similar manner, you can compute the areas of the other three triangles that are interior to the square but exterior to the original quadrilateral. Once you have all four areas, sum them and then subtract from the total area of the square. The result will be the area of the quadrilateral.
John
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