A Missing Edge Again
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 34 of 62.
The surface area formula can run backwards like the volume formula. With the surface area and two edges known, it becomes an equation for the third edge.
This box has surface area 62 and a base 3 by 2. The rule says 62 = 2 × (3 × 2 + 3 × h + 2 × h). Inside the bracket that is 6 + 5×h, so 62 = 12 + 10×h, then 50 = 10×h and h = 5.
The unknown edge appears in two of the three pairs of faces, which is why it shows up twice in the bracket. Collect those terms before you divide.
Challenge
The box has surface area 112 and a base 5 by 4. Write the equation from the figure and solve it for h.
Then press Check.
Try it yourself
Use the figure to find h
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: Pyramids7Surface Area of Prisms
Nets and Surface AreaVolume or Surface Area?A Missing Edge AgainTriangular PrismsThe Hidden Side FirstRecap: Prism Surfaces2Volume 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