The Slant Height
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 18 of 62.
Inside every right square pyramid (the apex straight above the centre of the base) there is a right triangle. Its upright side is the height, from the apex down to the centre of the base. Its bottom side runs from that centre out to the middle of a base edge, which is half the base edge. Its hypotenuse is the slant height, down the middle of a face.
This pyramid has base edge 6, so the bottom of the triangle is 3. With height 4, Pythagoras gives s^2 = 4^2 + 3^2 = 25, so the slant height is 5. The small square in the base marks the right angle that makes it work.
That is the rule Slant height: s^2 = h^2 + (b/2)^2. It links three lengths: the slant height, the height and the base edge. Watch the half: the triangle's bottom is half the base, not the whole of it.
Challenge
Three lengths of the pyramid glow: the slant height, the height and the base edge. Pick the rule that links them, then press Check.
Try it yourself
Name the rule that links them
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