Height From the Slant
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 19 of 62.
The slant height rule works in either direction. If you know the slant height and the base edge, it gives the height, and the height is what a volume needs.
This pyramid has base edge 16, so half of it is 8, and its slant height is 10. The rule says 10^2 = h^2 + 8^2, so h^2 = 100 - 64 = 36 and the height is 6. You subtract this time, because the slant height is the hypotenuse.
On the figure the height is marked ?. Tap it and pick Slant height: the engine solves the rule for the height.
Challenge
The pyramid's height is marked ?. Find it, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Surface Area & Volume
1Solids and Their Parts
Faces, Edges and VerticesPrisms and CylindersPyramids and ConesHeight or Slant Height?Spheres and HemispheresRecap: Parts of Solids4Pyramids
Volume of a PyramidThe Slant HeightHeight From the SlantHeight From the VolumeRecap: Pyramids2Volume of Prisms
Volume of a CuboidVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume3Cylinders
Volume of a CylinderHeight From the VolumeRadius From the VolumeEnough to Find It?Recap: Cylinders6Spheres and Hemispheres
Volume of a SphereHalf a SphereRadius From the VolumeSphere in a CylinderRecap: Spheres9Pyramids and Cones Outside
Surface of a PyramidSlant Height FirstSurface of a ConeThe Cone: Slant FirstRecap: Pyramid Surfaces