SOLUTION: how do i find the perimeter and area of a rectangle in the coordinate plane: L(0,1)M(3,5)N(5,5)P(5,1)

Question 156516This question is from textbook Geometry
: how do i find the perimeter and area of a rectangle in the coordinate plane:
L(0,1)M(3,5)N(5,5)P(5,1) This question is from textbook Geometry

Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
I think instead of:
L(0,1)M(3,5)N(5,5)P(5,1)
.
you meant:
L(3,1)M(3,5)N(5,5)P(5,1)
.
It would be best to plot all four points onto graph paper. Once you do that, it will be easy to see that:
width of the rectangle is between either:
LP or MN
.
whereas the length of the rectangle is between either:
LM or PN
.
Calculating the width. Let's use:M and N
M(3,5)N(5,5)
You can either see the distance visually from the graph or use the distance formula:
distance = sqrt[(x2-x1)^2 + (y2-y1)^2]
distance = sqrt[(5-3)^2 + (5-5)^2]
distance = sqrt[(2)^2 + (0)^2]
distance = sqrt[4 + 0]
distance = sqrt[4]
distance = 2 (width)
.
Calculating the length. Let's use:P and N
P(5,1)N(5,5)
You can either see the distance visually from the graph or use the distance formula:
distance = sqrt[(x2-x1)^2 + (y2-y1)^2]
distance = sqrt[(5-5)^2 + (5-1)^2]
distance = sqrt[(0)^2 + (4)^2]
distance = sqrt[0 + 16]
distance = sqrt[16]
distance = 4 (length)
.
Perimeter = 2(w+l) = 2(2+4) = 2(6) = 12 units
area = wl = 2(4) = 8 square units

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Well, this is an interesting problem for a tutor to solve. I don't mean the problem you stated, but the problem of what is wrong with your problem statement.

The difficulty is that quadrilateral LMNP is NOT a rectangle, it is a trapezoid. So the problem for me becomes trying to decipher whether you want to know how, in general, to find the perimeter and area of a rectangle that is described by four ordered pairs representing the vertices, or if you need help with finding the perimeter and area of trapezoid LMNP.

Quite frankly, I'm stumped. Write back and tell us what you really need.
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