APPENDIX A
FORMULAS DESCRIBING PLANE FIGURES AND SOLIDS
A-4. Prisms, Pyramids, Cylinders, and Cones
A-6. The Five Regular Polyhedra
A-l. The Trapezoid (sides a, b, c, d; a and b are parallel; the altitude h is the distance between a and b). The area S is given by
The trapezoid is a parallelogram if a = b and a rhombus if a = b = c = d.
A-2. Regular Polygons (length of side equal to a)
A-3. The Circle (radius r, see also Sec. 2.5-1). (a)
Circumference = 2πr area = πr2
(b) A central angle of φ radians subtends
(c) The area between a circle of radius r1 and an enclosed (not necessarily concentric) circle of radius r2 is π(r1 r2)(r1 — r2).
A-4. Prisms, Pyramids, Cylinders, and Cones. (a) Volume of a prism or cylinder (bounded by a plane parallel to the base of area S1, altitude h) hS1
(b) Volume of a pyramid or cone (base area S1, altitude h)
(c) Volume of the frustrum of a pyramid or cone (bounded by parallel planes; base areas S1, S2, altitude h)
(d) Curved surface area of a right circular cone (base radius r, altitude h)
A-6. The Five Regulur Polyhedra (length of side equal to a; the respective numbers F of surfaces, E of vertices, and K of edges are related by E + F − K = 2).
