Construction of an isosceles trapezoid given 3 different lengths.

Question

Given 3 different lengths, how do you construct an isosceles trapezoid when two of these lengths are bases and the other a side.

Answer 1

If you consider placing the two bases parallel to each other at a distance h, and with their centres also at a distance h, then h can be found as:

 h = sqrt(SL^2 - (B2-B1)^2/4)  

where:

• SL is the side length; and
• B1 and B2 are the two base lengths.

Answer 2

1. Draft the longer base.
2. Draw a circle from the midpoint of the base with radius the size of half of the shorter base. This circle intersects the longer base at two points.
3. Draw lines from these two points perpendicular to the longer base.
4. Draw circles with the radius of the length of the side of the trapezoid from either endpoint of the longer base.
5. These will intersect the two lines you drew perpendicular to the longer base at two points forming the missing two points of the trapezoid.
6. Draw in the trapezoid.