Triangular prism
The same triangle at both ends.
SolidFlat net
5 faces9 edges6 vertices
Volume
units3
V = BH
Triangular Prism vs Triangular Pyramid in 3D
Two triangular ends or one base and an apex? Rotate the complete shapes and compare their faces, nets, dimensions and measurements.
Triangular pyramid
Three side faces meet at one point.
SolidFlat net
4 faces6 edges4 vertices
Volume
units3
V = BH / 3
A net lays every face flat without stretching it. Use the slider below each shape to fold that net independently. The gold triangles mark the bases; dashed lines mark the hinges.
AssembledSeparated
Drag either shape to rotate both · Scroll or pinch to zoom · Arrow keys rotate
Change both shapes together
Same triangle. Same perpendicular height. Always.
Both bases are the same isosceles triangle. Its height t lies in the triangle. The solid height H is perpendicular to the base.
B = ½bt = units2
These models show a right prism and a pyramid with its apex over the base centroid. The pyramid is not generally a regular tetrahedron. Measurements use the displayed units.
From one triangle to the whole solid
Adjust the dimensions above to update every answer below. Start with the triangular base, then compare the space inside each shape and the area covering its surface.
The area of one base
B = ½ × 6 × 4 = units2
The triangle height t is measured within the base. It is different from the perpendicular solid height H.
Triangular prism calculator
Volume · space inside
units3
B × H = × 6
Total surface area
units2
2B + PH
2 triangular bases units2
1 rectangle · b × H units2
2 rectangles · s × H each units2
each
Lateral area PH units2
Lateral area counts the three rectangles only. Here each equal triangle side is s = √((b/2)² + t²) = , and the base perimeter P = b + 2s = .
Triangular pyramid calculator
Volume · space inside
units3
B × H ÷ 3 = × 6 ÷ 3
Total surface area
units2
B + A₁ + A₂ + A₃
1 triangular base units2
1 side triangle · ½bℓ₁
units2
2 side triangles · ½sℓ₂ each units2
each
Lateral area A₁ + A₂ + A₃ units2
The side-face heights are ℓ₁ = and ℓ₂ = . These are slant heights measured along the faces. Use perpendicular H for volume; use each face’s slant height for surface area.
How are these slant heights found?
The apex is directly above the base centroid, so ℓ₁ = √(H² + (t/3)²) and ℓ₂ = √(H² + (bt/(3s))²). The two slant heights generally differ. A single shared slant height works only when the base is equilateral in this centered model.
All lengths use the same unit. Areas use square units; volumes use cubic units. Results are rounded to two decimal places.
What actually changes?
| Compare | Triangular prism | Triangular pyramid |
|---|---|---|
| Triangular bases | Two congruent, parallel triangles | One triangle, opposite an apex |
| Faces | 5: 2 triangles + 3 rectangles* | 4: all triangles |
| Flat face netDashed lines are folds. |
|
|
| Edges / vertices | 9 edges / 6 vertices | 6 edges / 4 vertices |
| Volume |
V = BH units3 |
V = BH / 3 units3 |
| Total surface area |
S = 2B + PH units2 |
S = B + A₁ + A₂ + A₃ units2 |
| Parallel slices | Same triangle and area at every level | Smaller triangles toward the apex |
B is one triangular base area; P is its perimeter. A₁, A₂ and A₃ are the three pyramid side-face areas. *The side faces are rectangles for a right prism; they are parallelograms for an oblique prism.
Where can I see these shapes in real life?
A tent with triangular ends and a straight, level ridge approximates a triangular prism. A four-sided die is a familiar triangular pyramid: a regular tetrahedron. The adjustable pyramid above need not have equal edges, so it is more general than that die.
How many faces, edges and vertices does each have?
A triangular prism has 5 faces, 9 edges and 6 vertices. A triangular pyramid has 4 faces, 6 edges and 4 vertices. Use the edge and vertex views above to inspect them. Every edge is shared by two faces and is counted once.
Is a triangular pyramid a tetrahedron?
Yes. A tetrahedron has four triangular faces. A regular tetrahedron is a special case with four equilateral faces and six equal edges. Changing this pyramid’s height does not change its four-face structure.
Is a pyramid always one-third of a prism?
Only when their base areas and perpendicular heights are equal. That is why these models share both dimensions. Without those conditions, either solid could have the larger volume.
Keep the difference in view.
Two complete solids, the same triangle, and two different ways to enclose space. The reference brings the dimension labels, face counts, nets and volume formulas together.