DIMENSIONS OF PLANE FIGURES Machinery's Handbook, 31st Edition
78
Regular Polygon:
A = area
n = number of sides
α
360 ° n ÷ =
β
180 ° α – =
α
s 2 4 – --
ns 2 --- R 2
nsr 2 ----
s
= =
A
R
r
β
s 2 4 = + --
R 2 s 2 4 = – --
R r 2
2 R 2 r 2 – =
r
s
Example: Find the area of a polygon having 12 sides, inscribed in a circle with radius of 8 centimeters. The length of the side s is 4.141 centimeters. A ns 2 --- R 2 s 2 4 – -- 12 4.141 × 2 ------------- 8 2 4.141 2 4 – -------- 24.846 59.713 = = = 24.846 7.727 × 191.98cm 2 = =
Circle:
A = = = C = = = π r 2 2 π r
3.1416 r 2 6.2832 r
0.7854 d 2
Area
=
Circumference
=
3.1416 d
r C 6.2832 ÷ = d C 3.1416 ÷ =
A 3.1416 ÷ A 0.7854 ÷
=
=
0.564 A
d
r
=
=
1.128 A
Length of arc for center angle of 1° = 0.008727 d Length of arc for center angle of n ° = 0.008727 nd Example: Find area A and circumference C of a circle with a diameter of 2 3 ⁄ 4 inches. A 0.7854 d 2 0.7854 2.75 2 × 0.7854 2.75 × 2.75 × 5.9396in 2 = = = = C 3.1416 d 3.1416 2.75 × 8.6394in = = = Example: The area of a circle is 16.8 in 2 . Find its diameter. d 1.128 A 1.128 16.8 1.128 4.099 × 4.624in. = = = =
Sector of a Circle: l r α
r α 3.1416 180 ------------------ 0.01745 r α 2 A r ---- = =
Length of arc l
= =
Area A
= = = 57.296 l r ---------- = = α
1 ⁄ 2 rl 0.008727 α r 2
r 2 A l
---- 57.296 l α ---------- = =
Central angle, in degrees
,
Example: The radius of a circle is 35 millimeters, and angle a of a sector of the circle is 60 degrees. Find the area of the sector and the length of arc l . A 0.008727 α r 2 0.008727 60 × 35 2 × 641.41mm 2 6.41cm 2 = = = = l 0.01745 r α 0.01745 35 × 60 × 36.645mm = = =
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online