Any Triangle End
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 9 of 62.
The end of a prism does not have to be a right triangle. A tent has an end shaped like a roof, and its height is not one of its sides: it is the dashed line from the top straight down to the base, meeting it at a right angle.
Here the end has base 8 and height 3, so its area is 1/2 × 8 × 3 = 12. The prism is 10 long, so its volume is 12 × 10 = 120. The two slanted sides, 5 each, are there in the drawing, but the area of the end uses only the base and the height.
The rule is the same Volume of a prism. The trap is taking a slanted side for the height. The height is always the one at right angles to the base, marked with the small square.
Challenge
The tent-shaped prism has a triangle end with its height drawn dashed. Find the prism's volume, 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