Problem 1:A regular pentagon lamina of 30 mm side rests on HP with its plane surface vertical and inclined at 300 to VP. Draw its top and front views when one of its sides is perpendicular to HP.
Solution: The projections The pentagonal lamina has its surface vertical (i.e., perpendicular to HP) and inclined at 300 t oVP.Since the lamina is inclined to VP, initially it is assumed to be parallel to VP. In this position one of the sides of the pentagon should be perpendicular to HP. Therefore, draw a regular pentagon a'b'c'd'e' in the VP to represent the front view with its side a'e' perpendicular to HP. Since the lamina is perpendicular to HP, the top view will be a line, a(e)b(d)c. Assume that edge a’ e’ perpendicular to HP in the final position. The top view of the lamina is now rotated about a(e) such that the line is inclined at 30° to XY line, as shown by points a1,b1, c1, d1, and e1 in the right bottom of Figure 1. Draw vertical projectors from points a1,b1, c1, d1, and e1. Draw horizontal projectors from points a’, b’, c’, d’, and e’. The intersection gives the respective positions of the points In the Front view. Join a1’,b1’, c1’, d1’, and e1’ to obtain the Front view of the lamina.
Figure 1. Orthographic projections of the pentagonal lamina.