A square plate of side 60 mm is held on a corner on HP. Plate is inclined to the HP such that the plan of it is rhombuses with a diagonal of 30 mm. Determine the angle it makes with HP. The other diagonal is inclined at 45˚ to VP. Draw the projections of plate.

 Projection Of Plane

Projection of a Plane can be defined as visualizing the top view and the front view of the plane at certain positions. In this post are going to solve the following problem:

Question: A square plate of side 60 mm is held on a corner on HP. The plate is inclined to the HP such that the plan of it is rhombuses with a diagonal of 30 mm. Determine the angle it makes with HP. The other diagonal is inclined at 45˚ to VP. Draw the projections of the plate.

Solution: 

Procedure:

• As the first line of the question suggests, a square plate is held on a corner on HP (Horizontal Plane). It means we have to put the plate such that one of its diagonals is parallel to the XY line. The front view of the plate will be a straight line as shown in the solution.
• The second line says that the plate is inclined to the HP such that the plan (Top View) of it is rhombuses with a diagonal of 30 mm. This means we have to draw the top view such that the length of the diagonal which is parallel to the XY line is 30 mm (= 3 cm).
• Now, to draw the front view (Elevation) of the plate, we need to draw the projection of the top view (Plan) above the XY line. With the help of a compass, draw an arc of radius about ac. Mark all the necessary points according to the top view.
• The third line of the question says to determine the angle it makes with HP. It means we need to measure the angle of the front view (Which you drew in the previous step) making with the XY line. It should be around (69 ± 1)°.
• The fourth line of the question suggests that the other diagonal (Perpendicular to the XY line) is inclined at 45˚ to VP. It means we need to rotate the top view of the plate at an angle of 45°.
• Now, to draw the front view of the plate, we need to draw the projection of the top view and the front view of the plate. Mark all the necessary points according to the top view and the front view as shown in the solution.

I hope you understood the steps and the solution as well. If you have any doubts regarding to the solution or the question, let me know in the comment section. Till then keep learning, and keep improving!

Similar Questions:

1. A regular pentagon of 50 mm sides is resting on one of its sides on the H.P. such that it is parallel to and 25 mm in front of the V.P. If the highest corner of the pentagon rests in the V.P., draw its projections and find the angle made by the plane with the H.P.
2. A regular hexagonal plate 30 mm side is resting on one of its corners in V.P. the diagonal through that corner is inclined at 40° to V.P. and (i) if diagonal is inclined at 30° to H.P. (ii) if the plan of diagonal is inclined at 30° to H.P.