SOLUTION: Question: Given an isosceles triangle with a smaller base 0f 2, a perimeter of 70, and acute base angles of 60 degrees, find the trapezoid's area. Work done so far: I know the

 
Let the slanted sides of the trapezoid be X:

 

Draw in these two altitudes of the trapezoid, and
let their lengths be H:
 

 
Now we look at only the right triangle on the 
left, letting its bottom side's length be Z
 

 
Now we know that 
 
 and 
 
or
 
 and  
 
We also know that  and 
 
so
 
  and 
 
or
 
  and 
 
so we replace  by  and H by 
  


Now we go back to the trapezoid:
 


We know the small segment on the bottom is 2 because
the top side of the trapezoid is 2.  And we know that
the right segment on the bottom is also  because
the right triangle on the left and the one on the right 
are congruent.
 


Now we are told that the perimeter is 70.

So to form the perimeter, we add up all four sides of the 
trapezoid.

The left side of the trapezoid is 
The bottom side is this sum 
The right side is 
The top side is .

So the sum of all those must equal 70:



We solve that for X and get 22

So now we know that the bottom side is

 

and that is the larger base of the trapezoid.

And its height is .

Now we can find the area using , , and
, in the formula



.

Edwin