3 Three line segments of length 1 are joined together at

Last updated: 11/9/2023

3 Three line segments of length 1 are joined together at endpoints to form a base and the legs of an isosceles trapezoid as in Figure 3 Let 0 in 0 2 be the common angle measurement between the legs and the line passing through the base of length 1 We want to find the angle that maximizes the area of the trapezoid 1 1 Figure 3 An isosceles trapezoid with base and legs of length 1 a Compute the area A 0 of the trapezoid The general area formula for a trapezoid ish b b where h is the height and b and b2 are the lengths of the bases Hint Break up the trapezoid into a rectangle with two right triangles at both ends Use trigonometry to compute the height and the length of the longer base in terms of 0 b Find all solutions to A 0 0 with 0 0 2 Hint Write A 0 entirely in terms of cos 0 The answer is not 0 4 45 c Verify that the area A 0 is a maximum not a minimum at the angle found in part b and compute this maximum area