Pentagonal pyramid having side 25mm and axis length 60mm and the edge of the base of pentagonl pyramid on hp .
Draw the projection of pentagonal pyramid the axis of pyramid make 60°to hp4 parallel to v.p
The correct answer and explanation is :
To draw the projection of a pentagonal pyramid with the following details:
- Base side length = 25 mm
- Axis length = 60 mm
- The base of the pyramid is on the horizontal plane (HP).
- The axis of the pyramid makes a 60° angle with the HP and is parallel to the vertical plane (VP).
Here’s how the drawing and explanation would proceed:
Step-by-step process:
- First Projection (Top View – Plan):
- The base of the pyramid, which is a regular pentagon, will be represented in the top view.
- Since the pyramid’s base lies on the HP, draw the pentagon using the given side length of 25 mm.
- The vertices of the pentagon will be arranged symmetrically, and you can construct it using the standard method for creating a regular pentagon. First, draw a circle with a radius calculated based on the side length (side length ( s = 25 ) mm).
- Find the center of the pentagon and draw the 5 equal sides, ensuring the correct angles between them (108° for each internal angle in a regular pentagon).
- Second Projection (Front View):
- In the front view, the pyramid’s axis is inclined at 60° to the HP. This means the axis is represented as slanted at an angle to the ground.
- The apex of the pyramid (top point) will be above the center of the pentagonal base, and its distance from the base will be represented by the axis length (60 mm).
- Draw the axis line at a 60° angle to the horizontal line of the base in the front view. The height of the pyramid (60 mm) will be shown vertically along this axis.
- The edges of the pyramid from the apex to the base vertices will also be drawn, making sure they converge at the apex.
- Final Details:
- The edges connecting the apex to the base vertices are shown as lines in the front view.
- In the top view, the pentagonal base will be seen clearly, and the apex will be directly above the center of this base.
- Marking the axis properly at a 60° angle from the HP will help in creating a clear perspective of the pyramid’s shape.
Explanation:
- Top View (Plan): In this view, we see the regular pentagon as the base. Since the base lies on the HP, the top view will represent the base’s outline accurately.
- Front View (Elevation): The 60° inclination of the axis to the HP means the height of the pyramid is not directly vertical. This view shows the axis at an angle and the edges slanting from the apex to the base.
The pyramid’s projection involves using these projections to get a complete 3D representation of how the pyramid looks in space. These projections are orthogonal (perpendicular), allowing a clear understanding of the pyramid’s geometry from both the top and front perspectives.