Find the maximum possible area A of a trapezoid inscribed in a semicircle of radius 1, as shown in Fig. 3.7.17. Begin by expressing A as a function of the angle ? shown there.

Note: Ignore the question listed on the picture.

TC/2 FIGURE 3.7.17 A trapezoid inscribed in a semicircle (Problem 83). 4. A logger must cut a six-sided beam from a circular 1 of diameter 30 cm so that its cross section is as shown Fig. 3.7.18. The beam is symmetrical, with only two diff ent internal angles a and B. Show that the cross section maximal when the cross section is a regular hexagon, w equal sides and angles (corresponding to a = $ = 2x/ Note that a + 28 = 27t. (Why?)