SOLUTION: find the area and perimeter of a polygon with vertices A(1,2), B(2,-1), C(-1,-2), D(-2,1)

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Question 946623: find the area and perimeter of a polygon with vertices A(1,2), B(2,-1), C(-1,-2), D(-2,1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A(1,2), B(2,-1), C(-1,-2), D(-2,1)
first draw a polygon using given vertices:



find distance AB%7D%2C%7B%7B%7BAD%7D%2C%7B%7B%7BCD,

Thus in our case, the required distance is
d=sqrt%28%282-1%29%5E2+%2B+%28-1-2%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.



Thus in our case, the required distance is
d=sqrt%28%28-2-1%29%5E2+%2B+%281-2%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.

CD
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28-2--1%29%5E2+%2B+%281--2%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.



Thus in our case, the required distance is
d=sqrt%28%282--1%29%5E2+%2B+%28-1--2%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.


since all distances same => your polygon is a square and the length of its side is a=3.16227766016838
then the area and perimeter of this polygon will be:
A=a%5E2
A=%283.16227766016838%29%5E2
A=10
perimeter:
P=4a
P=4%2A3.16227766016838
P=12.64911064067352
P=12.65