Frustum:
            When a plane section is taken of a right prism parallel to its end (i.e., perpendicular to its axis), the section is known as a cross-section of the prism and the two positions of the prism are still prisms. If, however, the plane section taken is not parallel to the ends, the portion of the prism between the plane section and the base is called frustum.

Volume of a frustum of a Prism:
            In figure ABCEFGHI represents a frustum of a prism whose cutting plane EFGH is inclined at an angle  to the horizontal. In this case, the frustum can be taken as a prism with base ABEF and height BC.

(i)         Volume of the frustum  

        ABEF is a trapezium whose area is 
                                                           
        Volume of frustum                   
                                                           
i.e.         

Lateral Surface Area of a Prism:
            If the cutting plane is inclined at an angle  to the horizontal then from figure we have
           
or        
           
or        
or        

Hence
            Total surface area = area of the base + area of the section + lateral surface area

Note:   Lateral surface area of the frustum is the combination of rectangle and trapeziums whose area can be calculated separately.

Example:
            A hexagonal right prism, whose base is inscribed in a circle of radius 2m, is cut by a plane inclined at an angle of  to the horizontal. Find the volume of the frustum and the area of the section when the heights of the frustum are 8m and 6m respectively.

Solution:
            Area of cross-section   
            Here
        Area of base                
                                                
                                                

        Volume of frustum       
                                                

            Area of the section