Page 20 - Standard Handbook Of Petroleum & Natural Gas Engineering

Geometry 9

area = bh = ab sin c = 1/2 D,D, sin u
where u = angle between diagonals D, and D,

Trapezoid (Figure 1-7)

area = 1/2 (a + b)h'= 1/2 D,D, sin u
where u = angle between diagonals D, and D,
and where bases a and b are parallel.

Any quadrilateral (Figure 1-8)

area = 1/2 D,D, sin u
Note: a2 + b2 + c2 + d*= D2 + D* + 4m*
1 2
where m = distance between midpoints of D, and D,

Circles
area = nr2 = 1/2 Cr = 1/4 Cd = 1/4 nd2 = 0.785398d2
where r = radius
d = diameter
C = circumference = 2nr = nd