Pentagonal Pyramid Resting on a Triangular Face | Axis Appears 45° to VP | Projections of Solids

Learn how to draw the projections of a pentagonal pyramid resting on one of its slant triangular faces on HP, with its axis appearing inclined at 45° to VP, step by step on a grid sheet using only a scale, set squares, a protractor and a compass (no mini drafter). PROBLEM A pentagonal pyramid of base side 25 mm and axis length 60 mm is placed on one of its slant triangular faces on HP. Draw the projections of the pyramid if the axis appears to be inclined at 45° to VP. KEY IDEAS • "Appears inclined at 45° to VP" means the top view (plan) of the axis makes 45° with XY. • When a triangular face lies on HP, the axis inclination to HP is fixed by the shape of the pyramid: tan θ = (centre-to-edge distance) / (axis) = 17.2 / 60, so θ ≈ 16.0°. METHOD (three-stage / change of position method) • Stage I – Axis perpendicular to HP: base on HP, with the base edge ab of the resting face perpendicular to VP, so the face oab is seen as a line o'b' in the front view (its true slant height, 62.4 mm). The pentagon is drawn with the protractor (108° interior angles) and the scale. • Stage II – Tilt about edge ab until o'b' lies on XY. o1' is found by swinging the true length o'b' with the compass; c1'(e1') and d1' are located by intersecting compass arcs. • Stage III – Turn the pyramid about a vertical line until the top view of the axis is at 45° to XY. The 45° line is marked with the protractor; the apex o2 is stepped off with the compass, the corners are measured back from o2, and the perpendiculars for a, b, c, e are drawn with the 45° set square. • Final front view – vertical projectors from the final top view meet horizontal projectors from the stage II front view (heights do not change). KEY RESULTS • Axis inclination to HP: ≈ 16.0° (fixed by resting on a triangular face) • Top view of axis: 45° to XY (as given); true inclination of the axis to VP ≈ 42.8° • Hidden edges in the final top view: oa, ob • Hidden edges in the final front view: ab, de, ea, oa, oe CHAPTERS 0:00 Introduction 0:12 The problem (and why the axis is 16.0° to HP) 0:50 The three-stage approach (3D animation) 1:28 Instruments: scale, set squares, protractor, compass 1:45 Stage I – Top view (pentagon with the protractor) 2:44 Stage I – Front view and true slant height of the face 3:20 Stage II – Laying the face on XY with the compass 3:40 Stage II – Locating corners by intersecting arcs 4:25 Stage II – Top view 5:09 Stage III – Axis line at 45° with the protractor 5:38 Stage III – Transferring distances (divider and set square) 6:36 Checking by rotation and joining the final top view 6:58 Stage III – Final front view 7:48 Result and summary 8:13 Credits CREATED BY Dr. Yogeesha H C, Professor and Associate Director (IQAC) Nagarjuna College of Engineering & Technology (NCET) INSTRUMENTS USED Scale, 45° set square, 30°–60° set square, protractor, compass, HB pencil, grid sheet. Useful for first-year engineering students studying Engineering Graphics / Engineering Drawing (Projections of Solids). #EngineeringGraphics #EngineeringDrawing #ProjectionsOfSolids #PentagonalPyramid #OrthographicProjection