Rectangle ADEF and isosceles trapezoid FBCE both have a base of 12. The lower base angles of the trapezoid are 45° and the legs of the trapezoid are 6. How long is BC? Round your answer to the nearest tenth.

Question

anonymous · Answer

2. Draw FBCE with BC at the top, at FE as the base.
Draw lines straight down from B and C to FE, to form triangles with angles, 45, 45, 90. This is a 1:1:sqrt(2) triangle
the length of each of the sections is 6 / sqrt(2) = 3 * sqrt (2)
There are 2 of the triangles.
12 - 2 * (3 * sqrt (2))
= 12 - 6 sqrt(2)
= 12 - 8.485
= 3.5