Rich G. answered 03/20/19
This might be easier to solve by graphing, but that's not easy to do here so we'll do the equations.
We have the coordinates for 3 points, so this is a triangle. We have to find the distance between points D&E, E&F, and F&D to find the lengths of the sides.
Since D and E have the same x coordinate (-3), the distance from D to E is 3-1, or 2. So we can say line DE = 2
E and F have the same y coordinate (3), so the distance from E to F is 2-(-3) or 5. So line EF = 5
F and D have different x and y coordinates so we'll have to use the distance formula to find how long line FD is.
We'll say point 2 is F and point 1 is D, but it would work the other way too.
X2 = 2, X1 = -3, Y2 = 3, Y1 = 1
So d = √ (2-(-3))2 + (3-1)2
d = √52+ 22
d = √25+4
d = √29 ≈ 5.39
So line FD ≈ 5.39
Now we can find the perimeter by adding up the length of the three sides
P = DE + EF + FD
P = 2+5+5.39
P = 12.39
The area is found using the formula A = 1/2 bh
b = EF = 5
h = DE = 2
Plug those in to the equation and you'll find your area