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Calculate volume and surface area for triangular, rectangular, pentagonal, and hexagonal prisms
Volume: V = Base Area × Height
A prism is a 3D solid with two parallel, congruent polygon bases connected by rectangular faces. The bases can be any polygon (triangle, rectangle, pentagon, hexagon, etc.). Common examples include triangular prisms, rectangular prisms (boxes), and hexagonal prisms (pencils).
Volume = Base Area × Height. First, calculate the area of the base polygon using the appropriate formula for that shape. Then multiply by the height (the perpendicular distance between the two bases). This formula works for all prisms regardless of base shape.
A prism has two parallel bases of the same size connected by rectangular faces, while a pyramid has one base and triangular faces that meet at a single point (apex). Prism volume is Base × Height; pyramid volume is (Base × Height) / 3.
Surface Area = 2 × (Base Area) + (Perimeter of Base × Height). Calculate the base area, double it for both bases, then add the lateral surface area (perimeter of base times the height). This works for all prisms.
No, by definition a prism must have polygon bases. A solid with circular bases is called a cylinder. However, cylinders follow similar formulas: Volume = πr²h and Surface Area = 2πr² + 2πrh.
A right prism has bases perpendicular to the lateral faces (sides form 90° angles with bases). An oblique prism has bases at an angle, creating parallelogram lateral faces. Volume formula is the same for both, but oblique prisms have more complex surface area calculations.
Triangular prisms: roof trusses, Toblerone chocolate bars. Rectangular prisms: boxes, buildings, books. Hexagonal prisms: pencils, nuts and bolts. Pentagonal prisms: some buildings, bases of home plates in baseball.
Rearrange the volume formula: Height = Volume / Base Area. First calculate or measure the base area, then divide the known volume by that area to find the height. Ensure units are consistent.