🔺 Triangular Prism Calculator 2026
Calculate surface area, volume, and dimensions of triangular prisms
Enter Triangle Sides & Prism Length
a, b, c = triangle sides, L = prism length
📊 Results
Triangle Area
14.7 cm²
Triangle Perimeter
18 cm
Base Area (×2)
29.4 cm²
Lateral Area
180 cm²
Total Surface
209.4 cm²
Volume
147 cm³
📝 Step-by-Step Solution
Given: a=5, b=6, c=7 cm, L=10 cm
Semi-perimeter s = (5+6+7)/2 = 9
Triangle Area = √[s(s-a)(s-b)(s-c)] = √[9×4×3×2] = 14.70 cm²
Lateral Area = (a+b+c) × L = 18 × 10 = 180 cm²
Total Surface = 2×TriArea + Lateral = 29.39 + 180 = 209.39 cm²
Volume = TriArea × L = 14.70 × 10 = 146.97 cm³
📐 Triangular Prism Formulas
Triangle Area (Heron): A = √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2
Triangle Area (Base×Height): A = ½ × base × height
Lateral Surface Area: Alat = Perimeter × L = (a+b+c) × L
Total Surface Area: A = 2×TriangleArea + LateralArea
Volume: V = TriangleArea × L
Understanding Triangular Prisms
🔺 Shape
Two triangular bases + three rectangular faces. A prism with triangular cross-section. 6 vertices, 9 edges, 5 faces.
📐 Base Area
Heron's formula or ½bh. For any triangle, use Heron if you know 3 sides. Use ½bh if you know base and height.
📄 Lateral Area
Perimeter × Length. Sum of three rectangular faces. Each rectangle: one triangle side × prism length.
📦 Volume
Triangle Area × Length. Cross-section area times depth. Same principle as all prisms: base area × height.
Frequently Asked Questions
What is the surface area formula for a triangular prism?
A = 2×TriangleArea + Perimeter×L. Two triangular ends plus three
rectangular sides. Need triangle area (Heron or ½bh) and perimeter.
What is the volume formula for a triangular prism?
V = Triangle Area × Length. Cross-sectional area times prism
length. Same formula pattern as any prism.
What is Heron's formula?
A = √[s(s-a)(s-b)(s-c)]. Where s = (a+b+c)/2 (semi-perimeter).
Works for any triangle given three sides.
What is the lateral surface area?
Alat = (a+b+c) × L. Sum of three rectangular faces.
Perimeter of triangle times prism length.
How many faces does a triangular prism have?
5 faces. Two triangular bases (ends) and three rectangular lateral
faces. Also has 9 edges and 6 vertices.
What if I only know base and height?
Triangle Area = ½ × base × height. Then Volume = ½bh × L, Surface
= bh + (b + sides)×L. May need to estimate unknown sides.
What is an equilateral triangular prism?
Triangle base is equilateral (all sides equal). Area = (√3/4)s².
All three rectangular faces are congruent.
What is a right triangular prism?
Triangular base is a right triangle. Area = ½ × leg₁ × leg₂.
Common in roof trusses, wedges.
How do I find prism length from volume?
L = Volume / Triangle Area. Divide volume by cross-sectional area.
Need to calculate or know triangle area.
What are real-world examples of triangular prisms?
Toblerone boxes, tent shapes, roof trusses, some buildings, optical
prisms. Glass prisms split light into spectrum.
How do I find height of triangular base?
h = 2A/b. If you know area and base. Or use Pythagorean theorem
for specific triangles.
Can the triangular base be any shape?
Yes. Scalene, isosceles, equilateral, right triangle — any valid
triangle works. Formulas are the same.
What is an oblique triangular prism?
Bases not perpendicular to length. The prism "leans." Lateral
faces are parallelograms, not rectangles. Volume formula still works.
How does doubling length affect volume?
Volume doubles. V = A×L, so 2L gives 2V. Surface area increases by
ΔL × perimeter.
What is the cross-section of a triangular prism?
A triangle (the same as the base). Cutting perpendicular to length
always gives the same triangle.
How do I calculate net of triangular prism?
2 triangles + 3 rectangles. Total flat area = surface area.
Rectangles have dimensions: (side × L) for each side.
How accurate is this calculator?
Uses Heron's formula for precision. Handles any valid triangle.
Results are mathematically exact.