Volume measures the space inside a three-dimensional shape. A rectangular cereal box is a rectangular prism. A prism has two matching, parallel polygon ends called bases; a polygon is a flat shape with straight sides. Its volume is base area × perpendicular height, the distance between the bases measured at a right angle. For a rectangular box, this is length × width × height. One cubic inch is the space in a cube that is 1 inch long, 1 inch wide, and 1 inch tall.
A pyramid has one polygon base and triangular faces that meet at a point. Its height is the perpendicular distance from that point to the base, not a sloping edge. A pyramid has one third the volume of a prism with the same base area and height: V = (1/3) × base area × height.
A net is a flat pattern of faces that can fold into a solid. Total surface area adds the areas of all the faces, like the paper needed to wrap a box without overlaps. Lateral surface area counts the side faces but leaves out the bases. A prism has two matching, parallel bases; a pyramid has one. Name the bases first, because turning the shape does not change which faces they are.
