# Geometric Shapes - Areas

## Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

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### Square

*A = a ^{2} (1a)*

*a = A ^{1/2 } (1b)*

*d = a 2 ^{1/2} (1c)*

### Rectangle

A = a b (2a)d = (a^{2}+ b^{2})^{1/2}(2b)

### Parallelogram

A = a h

= a b sin α (3a)

d_{1}= ((a + h cotα)^{2}+ h^{2})^{1/2 }(3b)

d_{2}= ((a - h cotα)^{2}+ h^{2})^{1/2}(3b)

### Equilateral Triangle

*A = a ^{2}/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 a ^{2} 3^{1/2} (7a)*

*d = 2 a *

* = 2 / 3 ^{1/2} s *

* = 1.1547005 s (7b)*

*s = 3 ^{1/2} / 2 d *

* = 0.866025 d (7c)*

### Circle

A = π/4 d^{2 }

=^{ }π r^{2}

= 0.785.. d^{2}(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}r^{2}(9)

= 1/360 θ_{d}π r^{2}

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}) r^{2}

= 1/2 (π θ_{d}/180 - sin θ_{d}) r^{2 }(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 (r^{2}+ h^{2})^{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 r^{2}(13)

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