Welcome to the Interactive Pyramid Geometry Tool - a powerful and intuitive way to explore 3D shapes and understand the mathematics behind them. With this tool, you can build a pyramid with a polygon base of any number of sides and visualize how its geometry changes in real time.
Simply choose the number of vertices for the base, then drag and move each vertex - including the apex - to reshape the pyramid. The calculator instantly updates all key geometric properties: edge lengths, surface areas of each face, total surface area, and the volume of the pyramid.
To deepen understanding, the tool also provides detailed step-by-step calculations showing how each surface area, edge length, and volume is computed. This feature helps learners follow the mathematical process, not just see the results. (see FAQ section)
This interactive visualization is perfect for students learning solid geometry, teachers demonstrating spatial concepts, and anyone interested in architectural modeling or 3D design. Experiment, explore, and gain a deeper understanding of how shape affects size in three-dimensional space.
Tip: Drag vertices to move them. Drag apex vertically to change height. Drag empty space to rotate.
The volume \( V \) of any pyramid is given by the formula: \[ V = \frac{1}{3} A_{\text{base}} \times h \] where \( A_{\text{base}} \) is the area of the base and \( h \) is the perpendicular height from the base to the apex. Our tool calculates \( A_{\text{base}} \) even for irregular polygon bases and shows you every step of the computation.
The total surface area is the sum of the base area and the areas of all triangular faces. Each triangular face area is calculated as: \[ A_{\triangle} = \frac{1}{2} b \times s \] where \( b \) is the base edge length and \( s \) is the slant height of that face. The calculator automatically computes each face's area and shows the full breakdown step by step.
Yes. You can select any number of vertices \( n \) for the base - from triangles and squares to polygons with 10 or more sides. The tool dynamically adjusts calculations, surface areas, and volume based on your chosen shape.
Absolutely. Unlike most geometry calculators, this tool provides detailed step-by-step calculations for edge lengths, surface areas, and volume. This makes it ideal for students learning geometry, teachers explaining formulas, or anyone who wants to understand the math behind 3D shapes.
A pyramid with an \( n \)-sided polygon base has: