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Prism Calculator

Calculate volume, lateral surface area, total surface area, and base parameters for triangular, rectangular, and hexagonal prisms.

Prism Results
Volume
100
Total Surface Area
174.0312
Lateral Area
154.0312
Base Area (Single)
10
Deduction Steps:
Triangular Base: legs = 4, 5 → Area = ½ × 4 × 5 = 10
Prism Height H = 10
Base Perimeter: P = 15.4031
Volume: V = Base Area × H = 10 × 10 = 100
Lateral Surface Area: A_lat = P × H = 15.4031 × 10 = 154.0312
Total Surface Area: A_total = 2 × Base Area + A_lat = 2(10) + 154.0312 = 174.0312
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What Is a Prism Calculator?

A prism is a polyhedron comprising an n-sided polygonal base, a second translated copy of that base in a parallel plane, and n rectangular faces joining corresponding sides of the two bases.

How to Use This Calculator

  1. Select the base cross-section: Triangular, Rectangular, or Hexagonal.
  2. Enter base dimensions and prism height (H).
  3. View the calculated Volume, Total Surface Area, Lateral Surface Area, and Base Area.

Prism Volume and Surface Area Formulas

V = B \times H, \quad A_{\text{lat}} = P \times H, \quad A_{\text{total}} = 2B + A_{\text{lat}}

Volume is base area B multiplied by height H. Lateral area is base perimeter P multiplied by height. Total surface area adds both top and bottom bases.

Worked Example

Scenario: Find volume and surface area of a triangular prism with legs 3 and 4, height H = 10

Base Area: B = ½ × 3 × 4 = 6

Hypotenuse of base: √(3² + 4²) = 5

Base perimeter: P = 3 + 4 + 5 = 12

Volume: V = B × H = 6 × 10 = 60

Lateral area: A_lat = P × H = 12 × 10 = 120

Total area: A_total = 2(6) + 120 = 132

Result: Volume = 60, Total Surface Area = 132

Tips & Key Notes

  • A cylinder is effectively a prism with an infinite number of infinitesimal polygonal sides.
  • Lateral faces of a right prism are always rectangles perpendicular to the bases.
  • Volume depends strictly on base area and height, regardless of base shape.

Frequently Asked Questions

What defines a right prism?

In a right prism, the lateral joining edges are strictly perpendicular to the base planes.

How do you find the volume of any prism?

Multiply the cross-sectional area of the base (B) by the vertical prism height (H): V = B × H.

What is the difference between a prism and a pyramid?

A prism has two identical parallel bases connected by rectangular sides; a pyramid has one base tapering to a single apex vertex.

Is a cuboid considered a prism?

Yes, a cuboid is a right rectangular prism.

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