# Centroids of Plane Areas

The **centroid** of an area is the **point** where the whole area is considered to be concentrated.

### Square

#### Distance

*x = a / 2 (1a)*

*y = a / 2 (1b)*

#### Area

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

### Rectangle

#### Distance

*x = a / 2 (2a)*

*y = b / 2 (2b)*

#### Area

*A = a b (2c)*

### Circle

#### Distance

*x = r (3a)*

*y = r (3b)*

#### Area

*A = π r ^{2} (3c)*

### Semi-Circle

#### Distance

*x = 4 r / (3 π) (4a)*

*y = r (4b)*

#### Area

*A = π r ^{2}/ 2 (4c)*

### Right-angled Triangle

#### Distance

*x = b / 3 (5a)*

*y = h / 3 (5b)*

#### Area

*A = b h / 2 (5c)*

## Related Topics

### • Mathematics

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

## Related Documents

### Area Units Converter

Convert between units of area.

### 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.

### 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.

### Geometric Shapes - Areas

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

### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

### 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).

### Solids - Volumes and Surfaces

The volume and surface of solids like rectangular prism, cylinders, pyramids, cones and spheres - online calculator.

### Trigonometric Functions

Sine, cosine and tangent - the natural trigonometric functions.