1. **Stating the problem:** We have a pentagonal pyramid with a base side length of 30 mm and an axis length of 60 mm. The pyramid is positioned so that one of its slant edges lies on the horizontal plane, and the axis is parallel to the vertical plane. We need to draw its projections. 2. **Understanding the problem:** - The base is a regular pentagon with side 30 mm. - The axis (height from base to apex) is 60 mm. - One slant edge lies on the horizontal plane (HP). - The axis is parallel to the vertical plane (VP). 3. **Key concepts and formulas:** - The base pentagon can be constructed using the formula for the side of a regular pentagon. - The apex lies above the base at a height of 60 mm along the axis. - Projection involves orthographic views: top view (plan) and front view (elevation). 4. **Steps to draw projections:** - Draw the base pentagon in the top view with side 30 mm. - Mark one slant edge on the HP in the front view. - Since the axis is parallel to VP, the front view will show the true length of the axis (60 mm). - Project the apex vertically above the base center in the front view. - Draw the slant edges connecting the apex to the base vertices. 5. **Explanation:** - The top view shows the base shape and the position of the apex projected down. - The front view shows the height (axis length) and the slant edges. - The slant edge on HP means it appears as a true length in the front view lying on the horizontal line. Since this is a drawing problem, the exact graphical construction is required, which cannot be fully represented in text. However, the above steps guide the drawing process. **Final note:** This problem involves descriptive geometry and projection drawing techniques rather than algebraic calculation.