Square Pyramid Resting on a Slant Edge | Axis Appears 45° to VP | Projections of Solids

Learn how to draw the projections of a square pyramid resting on one of its slant edges 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 square pyramid of base side 25 mm and axis length 60 mm is placed on one of its slant edges 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 slant edge lies on HP, the axis inclination to HP is fixed by the shape of the pyramid: tan θ = (half diagonal) / (axis) = 17.68 / 60, so θ ≈ 16.4°. METHOD (three-stage / change of position method) • Stage I – Axis perpendicular to HP: base on HP, with the slant edge oa parallel to VP (diagonal ac parallel to XY), so o'a' shows the true length of the slant edge (62.6 mm). The square is drawn with the 45° set square resting on the scale. • Stage II – Tilt about corner a until o'a' lies on XY. o1' is found by swinging the true length o'a' with the compass; c1' and b1'(d1') are located by intersecting compass arcs (triangulation), so no angle measurement is needed. • 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 distances along the axis are stepped off with the compass as a divider, and the perpendicular for b and d is drawn with the 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: ≈ 16.4° (fixed by resting on a slant edge) • Top view of axis: 45° to XY (as given); true inclination of the axis to VP ≈ 42.7° • Hidden edge in the final top view: oa • Hidden edges in the final front view: cd, da, od CHAPTERS 0:00 Introduction 0:12 The problem (and why the axis is 16.4° to HP) 0:49 The three-stage approach (3D animation) 1:24 Instruments: scale, set squares, protractor, compass 1:41 Stage I – Top view (square with the 45° set square) 2:32 Stage I – Front view and true length of the slant edge 3:07 Stage II – Laying the slant edge on XY with the compass 3:25 Stage II – Locating corners by intersecting arcs 4:11 Stage II – Top view 4:50 Stage III – Axis line at 45° with the protractor 5:19 Stage III – Transferring distances (divider and set square) 6:01 Checking by rotation and joining the final top view 6:21 Stage III – Final front view 7:03 Result and summary 7:28 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 #SquarePyramid #OrthographicProjection