# Projection of Solids ( Problem 1)

## Problem – 1 Projection of Solids – A pentagonal pyramid has height 60 mm and the side of a base 30 mm. The pyramid rests on one of its sides of the base on the H.P. such that the triangular face containing that side is perpendicular to the H.P. and makes an angle of 45 degree with the V.P. Draw its projections.

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## Procedure:

Step-1 Draw a horizontal x-y line of some suitable length.

Step-2 Draw a pentagon of side of length 30 mm, below the x-y line at some suitable distance such that one side of the pentagon should be perpendicular with the x-y line, as shown into the figure. From the corners of the pentagon draw straight lines to the center of the pentagon, these lines represents the vertical slant edges of the pentagon converging at the center, in top view. And give the notations. It is the top view of the 1st stage.

Step-3 From the center of the pentagon in the top view i.e., point “ o ”, draw a vertical center line of the length equal to 60 mm.  And from the notations of the pentagon in top view, draw perpendicular vertical projectors up to the x-y line. From these end points draw slant lines connecting to the apex point  “ o’ ”  in the front view, and give the notations as shown into the figure. It is the front view of the 1st stage.

Step-4 Now copy the front view of the 1st stage as the front view of the 2nd stage with the same dimensions, such that the line o’a’, should be perpendicular to the x-y line, and the remaining drawing should be drawn accordingly as shown into the figure. It is the front view of the 2nd stage.

Step-5 From the notations of the front view of the 2nd stage draw vertical projectors into down ward direction and from the top view of the 1st stage draw projectors into horizontal direction as shown into the figure, Which will intersect with each other at respective points.

Step-6 From these respective points of intersections, draw straight lines between all the points in sequence as shown into the figure. It is the shape like a pentagon. And give the notations. It is the top view of the 2nd stage.

Step-7 Copy the top view of the 2nd stage as the top view of the 3rd stage, at an angle 45° with the x-y line such that the line ab should be inclined at the angle 45°, as show into the figure with the same dimensions. And give all the notations on it. It is the top view of the 3rd stage.

Step-8 From the front view of the 2nd stage, draw horizontal projectors, and from the top view of the 3rd stage draw vertical projectors in upward direction, which will intersect with the previously drawn projectors at respective points.

Step-9 From these respective points of intersections, draw straight lines between all the points in sequence as shown into the figure, It is the shape like a pentagonal pyramid, as shown into the figure. But the lines from the points d’ & c’ are dotted lines because of hidden. It is the front view of the 3rd stage.

Step-10 Give the dimensions by any one method of dimensions and give the notations as shown into the figure.

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