A square prism of side of base 30 mm, axis height 50 mm has its sides of base an equally incline with VP. A section plane perpendicular to the VP and inclined to the HP at 45 0 cuts the prism such that it passes through the point on the axis at a distance of 12 mm below the top base. Assuming the major part to be retained. Draw the projection of a prism showing the FV, sectional TV and true shape of section. Add development of lateral surface of the retained prism.

**Given Data:**

Side of prism = 30 mm

Axis length = 50 mm

Resting on HP with sides of equally inclined to VP.

A.I.P. inclined to HP at 45° and cut the prism axis at 12 mm below the top base.

**Procedure:**

**Stage 1: FV and Sectional TV**

Draw XY line.

Sides of prism are equally inclined to VP and it is resting on HP. So TV will be a square.

Now for equally inclined sides mark point 4 below XY line at some convenient distance. From Point 4 draw two lines inclined at 45° to XY line.

Taking 30 mm as radius and 4 as center cut this two lines. Mark that point 1 and 3.

Taking same radius and 1 as center draw an arc, keeping same radius and 3 as center draw another which will intersect the first arc. Mark the intersection point 2. Complete the square

Take the projection all corner points in FV, starting from XY line measure axis length 50 mm and complete the FV. Name the top base and bottom base as 1’2’3’4’.

For drawing AIP mark a point on center line at a distance of 12 mm below the top base. From that point draw a section line which is inclined 45° to horizontal.

Section line will cut the prism at different points such as if it cuts on vertical line 1’1’ name P1’ and if it cuts on base then name it a and b.

Take the projection of P1’, P2’P4’ and a’b’ in TV. Mark point P1, P2, P4, a and b in TV.

Join all these points P1, P2, a, b and P4. It shows the cut portion of prism. Hatch that part.

**Stage 2: True Shape of Section**

Draw the section line on left side of FV (take the measurement from FV P1’ to a’b’).

Mark all points on section line using compass such as P1’, P2’P4’ and a’b’.

Take the projection of above points in TV, below XY line.

From sectional TV take the projections of P1, P2, a, b and P4 towards left side.

Mark the intersection points and join all these points.

True shape of section (TSS) P1-P2-a-b-P4 will form. Hatch the TSS.

**Stage 3: Development**

On the right side of FV at some convenient distance take point 1’ , from 1’ draw a line equal to perimeter of square ( 4 x 30 mm). Divide it into 4 parts (Development).

Draw vertical lines from each points 1’, 2’, 3’, 4’ and again 1’. Name at both top as well as bottom base.

Take the projection of P1’, P2’, P4’ towards right side. Mark a and b point in development taking measurement from sectional TV.

Join P1-P2-a-b-P4-P1. Also draw other parts which is retained as continuous solid line.