Simulic
English

Cuboids and triangular prisms in 3D

Mathematics3D GeometryAges 12–13

Simulic.comLoading…

Use with my class

A cuboid (a × b × h) or a right prism whose base is a right triangle (legs a, b and height h) is drawn in space; drag to rotate it and see its faces, edges, and vertices. The lateral surface area, total surface area, and volume are calculated with formulas that update as you change the dimensions; turn on the net view to see the side faces unfold into a rectangle whose length equals the base perimeter. The 2D | 3D button switches to a true 3D view (WebGL): the solid with transparent faces, edges, vertex names and dimensions a, b, h; drag to rotate, scroll or pinch to zoom.

Lesson: Cuboids and cubes; right triangular and quadrilateral prisms

What it shows

A right prism has two congruent, parallel bases joined by rectangular side faces perpendicular to them; a cuboid is the special case with a rectangular base, and a cube has all edges equal. Unfolding the side faces gives one rectangle whose length is the base perimeter and whose width is the height, so the lateral surface area is perimeter × height. Adding the two bases gives the total surface area, and the volume is base area × height. For the prism with a right-angled triangular base, Pythagoras gives the hypotenuse needed for the perimeter.

How to use

Choose Cuboid or Triangular Prism and set Base edge a, Base edge b and Height h. Rotate the solid by dragging or with Auto-Rotate, and ask students to count faces, edges and vertices. Press Net to unfold the side faces and compare the length of the rectangle with the base perimeter. Ask students to predict how the volume and surface areas change when one dimension doubles, then check with the values shown.

Parameters you can change

  • Base edge a 1–10 cm
  • Base edge b 1–10 cm
  • Height h 1–10 cm
  • Solid Cuboid, Right triangular prism (right angle at B)
  • Auto-rotate

Questions to explore

  1. How many faces, edges and vertices does a triangular prism have, compared with a cuboid?
  2. If the height doubles, what happens to the volume and to the lateral surface area?
  3. With a = 3 and b = 4, how long is the hypotenuse of the prism's base, and what is its perimeter?

Related simulations