A pentagonal pyramid of 28 mm edge of base and 60 mm length of axis has a 28 mm edge on the H.P. The axis is inclined at $35^0$ to H.P. and $45^0$ to V.P. Draw the projections.
1 Answer

Q. 10

Given Data

Pentagonal Pyramid

Edge of base = 28 mm

Axis length = 60 mm

Resting 28 mm edge on HP

The axis is inclined 35° with HP

The axis is inclined 45° with VP

Stage 1

  1. Draw XY line.

  2. Pyramid is resting on HP, so pentagon will be in TV and triangle in FV.

  3. Draw TV as a pentagon (Side = 28 mm) with one edge of base perpendicular to VP (resting on edge of base).

  4. Name the pentagon 1 2 3 4 5.

  5. Take the projections of all corner points into FV.

  6. Complete the FV taking axis length 60 mm.

  7. Name the FV on base 1’ 2’ 3’ 4’5’ and apex point as O’.

Stage 2

  1. As axis is inclined at 35° to XY line (HP), the line 1’3’ will be inclined at 55° to XY line.

  2. So first mark point 3’4’ at some convenient distance on XY line. Then draw line 1’2’-3’4’ at angle of 55°, so that the axis will be inclined at 35°.

  3. Using compass mark centre point and draw the axis passing through it.

  4. Also mark point 2’ 5’ on that base line and draw slant edge.

  5. Complete the FV in inclined position using compass.

  6. Take the projections of all 5 points 1’2’3’4’ 5’ and O’ in TV.

  7. Take the horizontal projections of pentagon corner points towards right side.

  8. Mark intersection points as 1 2 3 4 5 and apex O.

  9. 3 sides of bases 2 3, 3 4 and 4 5 are not visible in TV. Also slant edges O 3 and O 4 not visible in TV. Draw these lines as hidden line.

  10. Draw remaining lines as continuous solid lines since they are visible in TV.

Stage 3

  1. Now in the axis is inclined to VP.

  2. Draw a line inclined at angle of 45° to XY line.

  3. Mark point O at some convenient distance below XY line.

  4. True length of axis is 60 mm, taking 60 mm in compass and O as centre, cut the line inclined at 45°. Mark that points O2.

  5. Take the horizontal projection of point O.

  6. Now taking O2 as centre and apparent length of axis (From the TV of 2nd stage) in compass as radius, cut the horizontal projection of O. Mark it O1.

  7. Using compass complete the TV in inclined position taking o 1 as apex point.

  8. Take the projection all points along with apex into FV.

  9. Take the projection all points along with apex towards right side from the FV of 2nd stage.

  10. Mark intersection points 1 2 3 4 5 and O.

  11. Draw base edges and slant edges.

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