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A square pyramid of 40 mm edge of base and 60 mm length of axis is resting in the HP on one of its base edges. The axis makes an angle of $30^0$ with the HP.

A square pyramid of 40 mm edge of base and 60 mm length of axis is resting in the HP on one of its base edges. The axis makes an angle of $30^0$ with the HP. Draw its projections if the top view of an axis is inclined at $45^0$to the VP.

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Q. 6

Given Data

Edge of base = 40 mm

Axis length = 60 mm

Resting on one of its base edge on HP

Axis inclination with HP = 30°

Top view of an axis is inclined 45° with VP

Procedure

Stage 1

  1. Draw XY line.

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

  3. Draw TV as a square with two sides parallel to VP.

  4. Name the square 1 2 3 4.

  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’ and apex point as O’.

Stage 2

  1. As axis is inclined at 30° to XY line (HP), the line 1’3’ will be inclined at 60° 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 60°, so that the axis will be inclined at 30°.

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

  4. Complete the FV in inclined position using compass.

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

  6. Take the horizontal projections of square corner points towards right side.

  7. Intersection of 1 and 1’ will give point 1, Intersection of 2 and 2’ will give point 2, Intersection of 3 and 3’ will give point 3, Intersection of 4 and 4’ will give point 4 and Intersection of O and O’ will give apex O.

  8. Side of base 3 4 will not be visible in TV. Draw this line as hidden line.

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

Stage 3

  1. Now in third stage the top view of an 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. (Don’t take it on XY line as it drawn in diagram wrongly)

  4. Using compass complete the TV in inclined position

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

  6. Take the projection all points along with apex towards right side from the FV of 1st stage.

  7. Mark intersection points 1 2 3 4 and O.

  8. Join base edges and slant edges.

  9. As slant edge O’4’ is not visible in FV, it will be hidden one.

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