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I98 MENSURATION.
divide this sum by the number of divisions (in Fig. 5 it is 8),
multiply this quotient by the length a &, and the product is the
area, approximately.
Note.—Sometimes the figure is of such shape that it is
more convenient to divide some of it into squares, rectangles,
or triangles, and figure the rest as explained above.
To Find the Area of a Sector of a Circle.
The area of a sector of a circle is to the area of the whole
circle as the number of degrees in the arc of the sector is to 360
degrees.
Thus
2
X £
360 2
A = r* X 3.1416 X a = .00S727 X r* X * = r ’
l=hA_
r
I = 3-1416 XflXr _ 0<01 745329 XaXr
180
r= Jj60A_ = JA_
> 3.1416 a * a
a = 180/ — 57.2956 /
3.1416 r r
A = Area of sector.
r = radius of sector.
a = number of degrees in arc.
/= length of arc in same units as A and r.
Example.
The arc of the sector (Fig. 6) is 60° na^
and the radius is 6 feet. Find area.
360 ._. 7T r2
60
"
Area
60r 2 7t
Area
Area =
360
60 X 6 X 6 X 3.1416
360
Area == 18.849 square feet.
If the length of the arc is known instead of the number of
degrees, multiply the length of the arc by the length of the
radius, divide product by 2, and the quotient is the area of the
sector. The correctness of this rule will be understood by the
rule for area of circles, explained under Fig. 4.
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