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.

X_{2} = 2, X_{1} = -3, Y_{2} = 3, Y_{1} = 1

So d = √ (2-(-3))^{2 }+ (3-1)^{2}

d = √5^{2}+ 2^{2}

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