Volume of a Pyramid - Dynamic GeoGebra Construction

Volume of a Pyramid - Dynamic GeoGebra Construction
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2017-02-12 21:26
This GeoGebra example demonstrates the volume of a pyramid (quadrilateral pyramid) through an interactive 3D construction, showing the base polygon, apex, and lateral edges. The core mathematical concept is the pyramid volume formula V = (1/3) × base area × height, along with spatial relationships among vertices, base, and edges. Construction highlights: the Polygon command creates the base quadrilateral (e.g., ABCD), PointIn places a point on the base, and Pyramid generates the solid from the base and apex; segments (Ribbe) and faces (zijvlak) label edges and lateral faces, while text (tekst1) displays the volume value. Suitable for middle or high school solid geometry lessons, this example helps students visualize how volume depends on base shape and height, and supports inquiry into volume formula derivation and dynamic manipulation of the pyramid's dimensions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → veelhoek1, a, b, c, d
  2. PointIn(e) → E
  3. Pyramid(veelhoek1, E) → f, zijvlakABE, zijvlakBCE, zijvlakCDE, zijvlakADE, RibbeAE, RibbeBE, RibbeCE, RibbeDE