Eng. ELSAYED FOUAD

Square

A = a² (1a)

a = A^1/2 (1b)

d = a 2^1/2 (1c)

Rectangle

A = a b (2a)
d = (a² + b²)^1/2 (2b)

Parallelogram

A = a h

= a b sin α (3a)

d₁ = ((a + h cot α)² + h²)^1/2 (3b)

d₂ = ((a - h cot α)² + h²)^1/2 (3b)

Equilateral Triangle

A = a²/3 3^1/2 (4a)

h = a/2 3^1/2 (4b)

Triangle

A = a h / 2

= r s (5a)

r = a h / 2s (5b)

R = b c / 2 h (5c)

s = (a + b + c) / 2 (5d)

x = s - a (5e)

y = s - b (5f)

z = s - c (5g)

Trapezoid

A = 1/2 (a + b) h

= m h (6a)

m = (a + b) / 2 (6b)

Hexagon

A = 3/2 a² 3^1/2 (7a)

d= 2 a

= 2 / 3^1/2 s

= 1.155 s (7b)

s = 3^1/2 / 2 d

= 0.866 d (7c)

Circle

A = π/4 d²

=π r²

= 0.785.. d² (8a)

U = 2 π r

= π d (8b)

Sector and Segment of a Circle

Sector of Circle

Area of a sector of circle can be expressed as

A = 1/2 θ_r r² (9)

= 1/360 θ_d π r²

where

θ_r= angle in radians

θ_d= angle in degrees

Segment of Circle

Area of a segment of circle can be expressed as

A = 1/2 (θ_r - sin θ_r) r²

= 1/2 (π θ_d/180 - sin θ_d) r²(10)

Right Circular Cylinder

Lateral surface area of a right circular circle can be expressed as

A = 2 π r h (11)

where

h= height of cylinder (m, ft)

r = radius of base (m, ft)

Right Circular Cone

Lateral surface area of a right circular cone can be expressed as

A = π r l

= π r (r² + h²)^1/2 (12)

where

h= height of cone (m, ft)

r = radius of base (m, ft)

l = slant length (m, ft)

Sphere

Lateral surface area of a sphere can be expressed as

A = 4 π r² (13)

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Monday, February 04, 2013

Areas of Geometric Shapes