Question 291815
Find the perimeter of the trapezoid with the dimensions below:

there is a picture but i cant draw it so here is an explaination.
slant height for both sides: 2
top width across: 3.5
bottom corner degrees on both sides: 60

*I DONT KNOW THE HEIGHT OR THE BOTTOM BASE.
<pre><font size = 4 color = "indigo"><b>

Here's the picture:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,2.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
line(-1.75,sqrt(3),1.75,sqrt(3)),locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),locate(-.3,sqrt(3)+.25,3.5),
locate(-2.4,1.1,2),locate(2.3,1.1,2)       )}}}

Now let's draw in two perpendiculars from the two upper
corners to the bottom base:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,2.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
line(-1.75,sqrt(3),1.75,sqrt(3)),locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),locate(-.3,sqrt(3)+.25,3.5),
green(line(-1.75,0,-1.75,sqrt(3))), green(line(1.75,0,1.75,sqrt(3))),
locate(-2.4,1.1,2),locate(2.3,1.1,2)
  )}}}

Now let's cut out the middle like this:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,-1.75,0),line(2.75,0,1.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),
green(line(-1.75,0,-1.75,sqrt(3))), green(line(1.75,0,1.75,sqrt(3))),
locate(-2.4,1.1,2),locate(2.3,1.1,2)
  )}}}

Now let's slide those two right triangles together, like this:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75+1.75,0,-1.75+1.75,0),line(2.75-1.75,0,1.75-1.75,0),
line(2.75-1.75,0,1.75-1.75,sqrt(3)), line(-2.75+1.75,0,-1.75+1.75,sqrt(3)),
locate(-2.55+1.75,.3,"60°"),
locate(2.2-1.75,.3,"60°"),
green(line(-1.75+1.75,0,-1.75+1.75,sqrt(3))), 
green(line(1.75-1.75,0,1.75-1.75,sqrt(3))),
locate(-2.4+1.75,1.1,2),locate(2.3-1.75,1.1,2)
  )}}}

Now we see that because of those two 60° angles,
that triangle is an equilateral triangle.  So its
bottom side is equal to its other two sides, making
the bottom side 2 also. so the two halves of the
bottom side of that triangle are 1 each, like this

{{{drawing(400,150,-3,3,-.25,2, line(-2.75+1.75,0,-1.75+1.75,0),line(2.75-1.75,0,1.75-1.75,0),
line(2.75-1.75,0,1.75-1.75,sqrt(3)), line(-2.75+1.75,0,-1.75+1.75,sqrt(3)),
locate(-2.55+1.75,.3,"60°"),
locate(2.2-1.75,.3,"60°"),
green(line(-1.75+1.75,0,-1.75+1.75,sqrt(3))), 
green(line(1.75-1.75,0,1.75-1.75,sqrt(3))),
locate(-2.4+1.75,1.1,2),locate(2.3-1.75,1.1,2),
locate(-.5,0,1),locate(.45,0,1)

  )}}}

Now slide them back apart:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,-1.75,0),line(2.75,0,1.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),
green(line(-1.75,0,-1.75,sqrt(3))), green(line(1.75,0,1.75,sqrt(3))),
locate(-2.4,1.1,2),locate(2.3,1.1,2),
locate(-.5-1.75,0,1),locate(.45+1.75,0,1)

  )}}}

Put the trapezoid back together like this:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,2.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
line(-1.75,sqrt(3),1.75,sqrt(3)),locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),locate(-.3,sqrt(3)+.25,3.5),
green(line(-1.75,0,-1.75,sqrt(3))), green(line(1.75,0,1.75,sqrt(3))),
locate(-2.4,1.1,2),locate(2.3,1.1,2),
locate(-.5-1.75,0,1),locate(.45+1.75,0,1)
  )}}}

Now we see that because the top base is 3.5, the
distance between the green lines at the bottom is
also 3.5:

{{{drawing(400,150,-3,3,-.25,2, line(-2.75,0,2.75,0),
line(2.75,0,1.75,sqrt(3)), line(-2.75,0,-1.75,sqrt(3)),
line(-1.75,sqrt(3),1.75,sqrt(3)),locate(-2.55,.3,"60°"),
locate(2.2,.3,"60°"),locate(-.3,sqrt(3)+.25,3.5),
green(line(-1.75,0,-1.75,sqrt(3))), green(line(1.75,0,1.75,sqrt(3))),
locate(-2.4,1.1,2),locate(2.3,1.1,2),
locate(-.5-1.75,0,1),locate(.45+1.75,0,1),locate(-.3,0,3.5) 
  )}}}

Now to find the perimeter, all we have to do is add up all
the pieces around the border of the trapezoid.

Bottom side = 1 + 3.5 + 1 = 5.5
Right slant side = 2
Top side = 3.5
Left slant side = 2

So the perimeter is 5.5 + 2 + 3.5 + 2 = 13

Edwin</pre>