Orthogonal projection and perpendicularity in practice
Answers are for parents and teachers.
1
A flat figure of area 80 lies in a plane at 60° to the horizontal. Find the area of its orthogonal projection onto the horizontal plane.
40
2
The base (projection) area of a roof is 72 m² and its slope is 45°. Find the roof’s surface area.
S = 72 / cos 45° = 72 · 2/√2 = 72√2 m².
3
A rectangular parallelepiped has dimensions 2, 10, 11. Find the longest straight rod that fits inside.
15
4
SA ⊥ (ABCD), ABCD is a square of side 8 and SA = 8. Find SC (use the fact that SA ⊥ AC).
AC = 8√2, SC = √(8² + (8√2)²) = √192 = 8√3.
5
Why does the 3-4-5 method give a correct check of a right angle between adjacent walls?
A triangle with sides 3, 4, 5 is right-angled by the converse of the Pythagorean theorem, since 3² + 4² = 5².