Determine all known information about the trapezoid, including the area, perimeter, lengths of other sides and angle measures.
Use the perimeter equation P= a + b + c + d to find the length of the base if the perimeter is known as well as the lengths of the other sides. Solve for the base.
Use the area equation A = height x (base a + base b)/2 if the area, height and one of the bases is known. Solve for the base using algebra to manipulate the equation.
Create a square or rectangle and two triangles inside the trapezoid by drawing two height lines from the end of the smaller parallel line to the longer one. Use the laws of sine, cosine and tangent (depending on the angles known) to determine the length of the rectangle side and the length of the sides of the triangles that are on the longer base. The laws of sine, cosine, tangent are equations that help you determine angles or lengths depending on the known information. For example, in the triangle created on the right end of the trapezoid, if hypotenuse is known as well as another angle, you can use the equation, sine of the angle = length of side opposite the angle/hypotenuse. For reference, sine = opposite/hypotenuse, cosine = adjacent/hypotenuse and tangent = opposite/adjacent. The phrase "Some Old Horse, Caught A Horse, Taking Oats Away" helps you remember the equations. Add the results -- the corresponding sides of the right triangles plus the length in between, which equals the smaller base -- together to determine the length of the long side.