The Hidden Side First
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 36 of 62.
The surface area needs every side of the triangle end, but a figure often gives only the two legs of a right triangle. The third side is not missing: the Pythagorean theorem fixes it.
Here the legs are 3 and 4, so the longest side is √(3^2 + 4^2) = 5. Now the surface area: the ends make 3 × 4 = 12 together, the rectangles make (3 + 4 + 5) × 2 = 24, and the total is 36.
On the board that is two steps. Tap the unlabelled side and pick Pythagorean theorem, then tap the prism and pick Surface area of a prism.
Challenge
The prism's ends are right triangles, but the longest side of the triangle is not labelled. Find the surface area, 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: 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