Page 299 - Industrial Process Plant Construction Estimating and Man Hour Analysis

Appendix D

Area and volume formulas

Formulas—areas and volumes
2
Square: area¼(edge) ;A¼a 2
Rectangle: base altitude; A¼ba
Right triangle: area¼1/2 base x altitude; A¼1/2 ba
Pythagorean theorem:
2
(Hypotenuse) +sum of squares of two legs of right triangle
2
2
2
2

c ¼ a +b ;a ¼ c b 2 ^ 1=2
Oblique triangle: area¼1/2 base altitude; A¼1/2 bh
^
A¼[s(s a)(s b)(s c)] 1/2, where s¼(a+b+c)/2
Parallelogram: opposite sides are parallel; A¼bh
Trapezoid: one pair of opposite sides parallel
A¼1/2 sum of bases x altitude; A¼1/2 (a+b) h
Circle: circumference¼2(pi) (radius)¼(pi) (diameter: C¼2(pi)R¼(pi)D
2
2
2
Area¼(pi) (radius) ¼(pi)/4) (diameter) :A¼(pi)R ¼(pi/4)D 2
2
Sector of circle: area¼1/2 radius arc; A¼1/2 Rc¼1/2 R angle
Segment of circle: area (segment)¼area (sector) area (triangle)
A¼Rc 1/2 ba
Ellipse: area¼(pi)ab
Parabolic segment: area¼2/3 ld
2
Right circular cone: V¼(pi)r h; A¼side area+base area
h i

2 2 ^
A ¼ piðÞrr + r +h 1=2
2
2
Right circular cylinder: V¼(pi)r h¼(pi)d h/4
A¼side area+end areas¼2 (pi)r (h+r)

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