Prism Calculator

Calculate volume, surface area, and other properties for different types of prisms. Supports triangular, rectangular, square, pentagonal, and hexagonal bases.

Base of the triangle

Height of the triangle

First side length

Second side length

Height of the prism (distance between bases)

Volume = Base Area * Height Total Surface Area = 2 * Base Area + Lateral Area Lateral Area = Base Perimeter * Height Base Area Formulas: • Triangle: ½ * base * height • Rectangle: length * width • Square: side^2 • Pentagon: (5 * side^2 * tan(PI/5)) / 4 • Hexagon: (3sqrt3 * side^2) / 2 Where: Height = distance between parallel bases Lateral faces = rectangular sides connecting bases
Example 1 (Triangular Prism): Base = 6 cm, Triangle Height = 4 cm Sides = 5 cm, 5 cm (isosceles) Prism Height = 10 cm Base Area = ½ * 6 * 4 = 12 cm^2 Perimeter = 6 + 5 + 5 = 16 cm Volume = 12 * 10 = 120 cm^3 Lateral Area = 16 * 10 = 160 cm^2 Total SA = 2(12) + 160 = 184 cm^2 Example 2 (Rectangular Prism): Length = 8 cm, Width = 5 cm Height = 10 cm Base Area = 8 * 5 = 40 cm^2 Volume = 40 * 10 = 400 cm^3 Lateral Area = 2(8+5) * 10 = 260 cm^2 Total SA = 2(40) + 260 = 340 cm^2 Example 3 (Hexagonal Prism): Side = 4 cm, Height = 10 cm Base Area = (3sqrt3 * 16) / 2 = 41.57 cm^2 Volume = 41.57 * 10 = 415.7 cm^3

What is a prism in geometry?

A prism is a 3D solid with two identical parallel polygonal bases connected by rectangular lateral faces. The number of lateral faces equals the number of sides in the base. Examples: triangular prism (3 lateral faces), rectangular prism (4 lateral faces), pentagonal prism (5 lateral faces).

What are the formulas for a prism?

Volume = Base Area * Height. Surface Area = 2 * Base Area + Lateral Area. Lateral Area = Perimeter of Base * Height. The formulas work for any prism regardless of base shape (triangular, rectangular, pentagonal, etc.).

What is the difference between a right prism and an oblique prism?

A right prism has lateral edges perpendicular to the base (vertical sides), making lateral faces rectangles. An oblique prism has slanted lateral edges, making lateral faces parallelograms. This calculator assumes right prisms. Volume formula is the same for both types.

How do you calculate the base area for different prism types?

Triangle: ½ * base * height. Rectangle: length * width. Square: side^2. Regular polygon: (Perimeter * Apothem)/2. Circle (cylinder): PIr^2. For irregular bases, break into triangles or use coordinate geometry. This calculator supports common regular shapes.

What are real-world examples of prisms?

Buildings and rooms (rectangular prisms), roof trusses (triangular prisms), pencils (hexagonal prisms), Toblerone chocolate (triangular prism), shipping containers, books, bricks, packaging boxes, crystals, and structural beams. Prisms are everywhere in architecture and engineering.

What is the difference between a prism and a pyramid?

A prism has two identical parallel bases and constant cross-section throughout its height. A pyramid has one base and sides that meet at a single apex point. Volume: Prism = Base Area * Height, Pyramid = ⅓ * Base Area * Height (pyramid is ⅓ of prism).

How do you find the height of a prism if you know the volume?

Rearrange the volume formula: Height = Volume / Base Area. Example: A triangular prism with volume 60 cm^3 and base area 12 cm^2 has height = 60/12 = 5 cm. You need to know both volume and base area.

What is lateral surface area vs total surface area?

Lateral surface area is only the area of the side faces (excluding top and bottom bases). Total surface area includes the two bases plus all lateral faces. Formula: Total SA = Lateral SA + 2 * Base Area. Useful for calculating material needed for sides vs entire surface.