SOLUTION: Find the area and perimeter of the quadrilateral whose vertices are (4,7),(1,4),(4,1) and (7,4)

Algebra ->  Geometry-proofs -> SOLUTION: Find the area and perimeter of the quadrilateral whose vertices are (4,7),(1,4),(4,1) and (7,4)       Log On


   

Question 985946: Find the area and perimeter of the quadrilateral whose vertices are (4,7),(1,4),(4,1) and (7,4)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Understanding the figure very clearly will come from plotting those four points. Any tests you want, ... the figure is square. Test slopes at the intersection points, test with Distance Formula point to point around the figure. Perimeter is four times length of any single side.

Point (1,4) and (7,4) is a diagonal of the square serving as base of an upper and a lower triangle. This base is 7-1=6. Either triangle has "altitude" 4-1=7-4=3.
Area is then, for the square figure, base%2Aheight=6%2A3=18.