# Geometric Shapes - Areas

### Square

The area of a square can be calculated as

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

The side of a square can be calculated as

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

The diagonal of a square can be calculated as

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

### Rectangle

The area of a rectangle can be calculated as

*A = a b (2a)*

The diagonal of a rectangle can be calculated as

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

### Parallelogram

The area of a parallelogram can be calculated as

*A = a h *

* = a b sin α (3a)*

The diameters of a parallelogram can be calculated as

*d _{1} = ((a + h cot α)^{2} + h^{2})^{1/2 } (3b)*

*d _{2} = ((a - h cot α)^{2} + h^{2})^{1/2} (3b)*

### Equilateral Triangle

An equilateral triangle is a triangle in which all three sides are equal.

The area of an equilateral triangle can be calculated as

*A = a ^{2}/3 3^{1/2} (4a)*

The area of an equilateral triangle can be calculated as

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

### Triangle

The area of a triangle can be calculated as

*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

The area of a trapezoid can be calculated as

*A = 1/2 (a + b) h *

* = m h (6a)*

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

### Hexagon

The area of a hexagon can be calculated as

*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

The area of a circle can be calculated as

*A = π/4 d ^{2}*

* = π r ^{2} *

* = 0.785.. d ^{2} (8a)*

*C = 2 π r *

* = π d (8b)*^{}

*where *

*C = circumference*

### 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)*

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Area of Intersecting Circles

Calculate area of intersecting circles

### Area Units Converter

Convert between units of area.

### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

### Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.

### Circle Equation

The equation for a circle

### Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.

### Circles Outside a Circle

Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.

### Cylindrical Tanks - Volumes

Volume in US gallons and liters.

### Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.

### Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.

### Exponents - Powers and Roots

The laws of fractional and integer exponents.

### Factorials

The product of all positive integers.

### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

### Oblique Triangle

Calculate oblique triangles.

### Pythagorean Theorem

Verifying square corners.

### Right Angled Triangle

Right angled triangle equations.

### Smaller Rectangles within a Larger Rectangle

The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).

### Squaring with Diagonal Measurements

A rectangle is square if the lengths of both diagonals are equal.

### Trigonometric Functions

Sine, cosine and tangent - the natural trigonometric functions.