Prisms: problems with angles and diagonals
Find the height and the lateral edge of a right prism from a diagonal and an angle, work out the lateral area and give answers with a root.
- Ukraine: grade 11
- Russia: grade 10
Guide
In the Ukrainian programme this is Grade 11 geometry: §16 "Prism" (problems 6-8) and §25 "Revision of the geometry course" (problems 99-102). The textbook letters: prism ABCA₁B₁C₁, b the lateral edge, h the height, Sб the lateral area (S for "бічна"), Pосн the perimeter of the base.
Lateral-area theorem. The lateral area of a right prism is the perimeter of its base times the lateral edge: Sб = Pосн·b. In a right prism the lateral edge is the height and the side faces are rectangles.
The angle between a line and a plane is the angle between the line and its projection on the plane. Almost every problem reduces to a right triangle: find its sides with Pythagoras or with the tangent of the angle.
All lengths are in centimetres. Type an answer with a root, such as 3√2, with the √ button.