HOW TO MEASURE AN AREA
ELLIPSE
If the geometric shape resembles an ellipse rather than a
circle, the formula A = 0.7854 x a x b is used, with a
representing the length of the ellipse and b the shorter
length or what may be considered its width.
a
15 ft.
b
5 ft.
Formula:
A = 0.7854 x a x b, where
a = length of the ellipse, and
b = shorter dimension (width)
Example: a = 15 ft.
b = 5 ft.
A = 0.7854 x 15 x 15 = 58.9 sq. ft.
IRREGULARLY-SHAPED AREA
Method I. Determination of a very irregularly shaped area
can be obtained by establishing the longest line possible
lengthwise throug the center of the area. Numberous lines
are then established perpendicular to this center line. The
total number of lines will depend upon how irregular the
shape of the area may be. The more irregular it is, the
more lines should be drawn. From the average length of
all these lines, the width of the area is determined and the
area calculated as a rectangle.
Method II. Another method for determining the size of an
irregularly-shaped area, a golf green, fro example, is to
establish a point as near to the center of the area as can
be estimated. From this point, as with a compass, distances
for each 10-degree increment are measured to the edge
of the irregularly shaped green. Then, the 36
measurements taken completely around the central point
are averaged. The idea is to obtain an average
measurement, and that measurement becomes the radius
of the circle. The diameter (d) of the circle is found by
multiplying its radius by 2. The area then is computed using
the formula for a circle.
Formula:
A = a x b, where
a = distance between A and B, and
b = average of all lengths a’ to j’
(lines are drawn perpendicular to a)
Example:
a’ = 10 ft.
b’ = 14 ft.
c’ = 18 ft.
d’ = 35 ft.
e’ = 13 ft.
f’ = 30 ft.
g’ = 23 ft. a = 128 ft.
h’ = 20 ft. b = 18.6 ft. (186 10)
i’ = 15 ft. A = 2380.8 sq. ft. (128 x 18.6)
j’ = 8 ft.
Total 186 ft.
Formula:
A = 0.7854 x d x d, where d = average r x 2
Example:
Degrees Distance (ft.):
10 (r
1
) ..................................... 54.8
20 (r
2
) ..................................... 43.9
30 (r
3
) ..................................... 48.4
40 (r
4
) ..................................... 46.9
330 (r
33
) ..................................... 41.5
340 (r
34
) ..................................... 48.6
350 (r
35
) ..................................... 51.0
360 (r
36
) ..................................... 50.0
Total 1980.0
r = 55 (1980 36)
d = 110 (r x 2)
A = 9503.34 sq. ft. (0.7854 x 110 x 110)
