Calculate volume, lateral surface area, total surface area, and base parameters for triangular, rectangular, and hexagonal prisms.
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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.
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.
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
In a right prism, the lateral joining edges are strictly perpendicular to the base planes.
Multiply the cross-sectional area of the base (B) by the vertical prism height (H): V = B × H.
A prism has two identical parallel bases connected by rectangular sides; a pyramid has one base tapering to a single apex vertex.
Yes, a cuboid is a right rectangular prism.
Calculate cuboid (rectangular prism) volume, total surface area, lateral area, and space diagonal from length, width, and height.
Calculate right circular cylinder volume, total surface area, lateral (curved) surface area, and base area from radius and height.
Calculate pyramid volume, total surface area, lateral area, and slant heights for square and rectangular pyramids with step-by-step steps.