 I am going to teach you about development of the lateral surface of a pentagonal prism. At the end of this session, students will be able to draw the lateral surface of a regular prism. So in this figure, this is a prism, a pentagonal prism. So in this, it is having two pentagonal surfaces, one is arranged at the top and another is arranged at the bottom. And they both are parallel to each other and they are at a distance that is equal to axis height or that is called as height of the prism. And in the first figure, we are seeing that so it is having five corners first of all. So five edges of this much length. Since it is having five edges, the opposite edges of the opposite surfaces are going to be connected with the rectangular surface called vertical surface. And this is nothing but the vertical edge in the prism and the length of this equal to the axis of the height. To obtain the development of the prism, we need to cut this surface at one vertical edge. So in this figure, I am going to cut this edge. So in the second figure, we are going to that by it as an opening or it is unrolling so that we can place it on the development plane. So all five vertical rectangles are to be kept on the development plane. So that we get this type surface called development of the prism and the length of this line is equal to the five times the edge of the pentagonal surface. And the height of this rectangle is equal to the axis height. Here we get two pentagonal surfaces, one is for top surface and another is for the bottom surface. So we take one example in this regular pentagonal prism is kept on HP that is horizontal plane so that the true shape of the pentagonal surface will come on the top view that is on HP. So this plane above XY line is VP plane and this below XY line is called as VP plane. Here so this line is indicating with the XY line. So in this we need to draw the front view and here we have drawn the top view. So it is having 30mm base edge and the height of this prism is equal to the 70mm and this is 30mm. So at this 30mm, the cutting plane is passing through the axis. Now since it is resting on HP, so we get the pentagonal surface on the top view with its true shape. And since it is having two pentagonal surfaces, we need to name one bottom pentagonal surface with the name PQRST and the top pentagonal surface with A, B, C, D, E. So since we have cut this pentagonal prism at the vertical edge PA, so for the full pentagonal prism so as we discussed in this slide so it is having full axis height and the length of this equal to 5 times the edges. So here similar without cutting the prism so we get this P to P and P to A and again A and P. So this we get as a development of the prism for full prism. Now if it is cut, we get this type of profile that is a surface. So here this is nothing but the front view of the object. So here we use one cutting plane which is cutting the prism axis at a height of 30mm above the HP. So this dark line figure is nothing but the front view of the truncated prism. So from this point we need to project here we get this vertical edge here and this vertical edge here. So here basically one first vertical edge P to A and this one is T to 5 and this is Q to 2 and it is S to 4 and it is R to 3. So these are the vertical edge we get in the front view. Now here the cutting plane is at an angle of 45 degree with HP. So this incline will come as a cutting edge in the front view. So these are the points of intersection with the cutting plane and the vertical edge of the prism. We need to name this with different namings that has 1, 2 here, 3 here, 4 here and 5 here. So why we need to mark of 2 point here because since PA edge is here and if you take it is in this direction. So this Q to 2 vertical edge will come first. So we need to mark this with point number 2 and for this vertical edge so point number 3 and from this point this vertical edge will come. So what is with the point number 4 and this with the point number 5. Now so already we have drawn the development of that surface for the full prism. So after this marking of the intersection points we need to transfer this on the vertical edges that has been drawn in this surface. Here this intermediate vertical edges has to be drawn at an distance of 30 mm because this length is equal to 30 mm, 30, 30, 30, 30. So this total is 150 length. So it has to be divided by 5 times. So name that with a PQRST because we have cut this prism at vertical edge that is PA. So transfer this point number 1. So since it is on PA vertical edge so transfer this on PA. So we get this point here and we get this point here because here one more PLN is there. Next point number 2 is on QB. So we need to transfer this on QB line. So point number 3 is here so transfer this on RC vertical edge. So we get this point as point number 3. So point number 4, this point is on SD so transfer this point on SD vertical edge. So we get this point here and similarly point number 5 is here so transfer this point on TE. So we get intersection point for 5 is here. Now after getting these points so connect these points with a straight line. So straight line because the pentagonal prism is a flat surface that the rectangle surface or the flat surface. So once it is cut we get a inclined edges with a straight line. So that we need to connect these points with a straight lines. 1, 2, 3, 4, 5 and 1. And again for this dark line up to this connect with this point. And these vertical edges also also draw with a dark line. So now this surface with a dark line indicates that this is the development of the lateral surface of the truncated prism. So now and once it is cut so from this point so from this direction of weaving so if the observer is here. So to draw the true shape of this cut object so the observer must be here. So before that we need to draw one more x1, y1 line here. This is parallel to this inclined edge. So to draw the true shape of this surface we need to transfer the projections from 1, 5, 2, 4 and 3 which are perpendicular to this intersection plane that is x1, y1. So from this point of intersections we need to transfer this height below xy up to the point 1, 2, 3, 4 and 5. So transfer these points here. So from this point so point number 1 is at this much distance. So from this point since it is a point number 1 in this projection so transfer this height from this point so it will we will get one point here. So similarly point number 2 from this point up to this we need to measure with a compass and from this point because this is a point number 2 projection. So from this point we need to cut an arc on this projection. So similarly point number 3 this is a point number 3 projection. So cut this much distance on this projection. So similarly 4 and 5 distance has to be cut on this. So join these points to get it as a true shape of this surface from the top view. And this view is called as auxiliary top view. This is a true shape of this cut object. And we can let you think that what might be the profile or the surface. So if the direction of the cutting plane is reversed in this direction if it is. Or if the inclination of the cutting plane changes to 30 degree. Either the profile is same or not. Let you think. This is the reference I used. Thank you.