Draw the projection of pentagonal pyramid 40mm side and axis 70mm long if it is resting on one of its base edges with axis making an angle of 30° to HP and axis makes an angle of 45° xy line
Engineering Graphics
ScanSolve AI Answer
Step-by-step solution
3 stepsHere are the steps to draw the projections of the pentagonal pyramid:
Initial Position - Base on HP, one base edge perpendicular to VP
- Draw the XY line. This represents the intersection of the Horizontal Plane (HP) and Vertical Plane (VP).
- Draw the Top View (TV):
- Draw a regular pentagon with a side length of 40 mm. Since the pyramid is resting on one of its base edges, and for simplicity in the next stage, orient the pentagon such that one base edge is perpendicular to the XY line (or parallel to VP). Label the base corners A, B, C, D, E.
- Locate the center of the pentagon, which is the projection of the apex (O) and the center of the base (o).
- Draw lines from the center to each corner of the pentagon to represent the slant edges.
- Draw the Front View (FV):
- Project all corners of the pentagon (A, B, C, D, E) from the top view onto the XY line. These points will be a', b', c', d', e' on the XY line.
- From the center 'o' in the top view, project a line perpendicular to the XY line. Measure 70 mm (axis length) upwards from the XY line along this projection to locate the apex o'.
- Connect o' to the visible base corners on the XY line (a', b', c', d', e'). The visible edges will be solid lines, and hidden edges (if any) will be dashed. In this orientation, the front view will be an isosceles triangle with its base on the XY line.
Inclination to HP - Axis at 30° to HP
- Redraw the Front View (FV):
- Since the pyramid is resting on one of its base edges (let's say A'B'), this edge will remain on the XY line.
- Redraw the entire front view from Step 1, rotating it such that the axis o'o (the line from the center of the base to the apex) makes an angle of 30° with the XY line. The base edge A'B' will be on the XY line.
- Label the new positions of the base corners and apex as a'1, b'1, c'1, d'1, e'1, and o'1.
- Draw the Top View (TV):
- Project vertical lines downwards from each point (a'1, b'1, c'1, d'1, e'1, o'1) of the new front view.
- Project horizontal lines from the corresponding points (A, B, C, D, E, O) of the initial top view (from Step 1).
- The intersection of these projection lines will give the new top view points (A1, B1, C1, D1, E1, O1).
- Connect the base points A1, B1, C1, D1, E1 to form the base.
- Connect the apex O1 to all base points to form the slant edges.
- Determine visibility: Edges closer to the observer (when looking from the top) are solid. Hidden edges are dashed. The base edge on which it rests (A1B1) will be visible.
- Redraw the Front View (FV):
Inclination to VP - Top view of axis at 45° to XY line
- Redraw the Top View (TV):
- Take the top view obtained in Step 2.
- Identify the projection of the axis (the line O1o1, where o1 is the center of the base in the top view).
- Redraw this entire top view such that the line O1o1 makes an angle of 45° with the XY line.
- Label the new positions of the base corners and apex as A2, B2, C2, D2, E2, and O2.
- Draw the Final Front View (FV):
- Project vertical lines upwards from each point (A2, B2, C2, D2, E2, O2) of the new top view.
- Project horizontal lines from the corresponding points (a'1, b'1, c'1, d'1, e'1, o'1) of the front view from Step 2.
- The intersection of these projection lines will give the final front view points (a'2, b'2, c'2, d'2, e'2, o'2).
- Connect the base points a'2, b'2, c'2, d'2, e'2.
- Connect the apex o'2 to all base points to form the slant edges.
- Determine visibility: Edges closer to the observer (when looking from the front) are solid. Hidden edges are dashed. The base edge on which it rests (a'2b'2) will be visible.
- Redraw the Top View (TV):
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