What is the formula for area?
Perimeter, Area, and Volume
| Table 2. Area Formulas | ||
|---|---|---|
| Shape | Formula | Variables |
| Square | A=s2 | s is the length of the side of the square. |
| Rectangle | A=LW | L and W are the lengths of the rectangle’s sides (length and width). |
| Triangle | A=12bh | b and h are the base and height |
Who invented shoelace formula?
Albrecht Ludwig Friedrich Meister
It is also sometimes called the shoelace method. It has applications in surveying and forestry, among other areas. The formula was described by Albrecht Ludwig Friedrich Meister (1724–1788) in 1769 and is based on the trapezoid formula which was described by Carl Friedrich Gauss and C.G.J. Jacobi.
How do you find the area of polygons?
To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon’s center to the midpoint of any side that is perpendicular to that side.
What is a formula of area of square?
The area of a square is calculated with the help of the formula: Area = s × s, where, ‘s’ is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units.
Why is the area of a square a side square?
Why is the area of a square a side square? A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.
Why does the shoelace formula work?
The shoelace formula works because of the ability to add these oriented areas without having to specify which ones to subtract. It amounts to decomposing a shape into a list of triangles with the origin as the third vertex, and adding their areas.
What is the simplest polygon?
In geometry, a simple polygon /ˈpɒlɪɡɒn/ is a polygon that does not intersect itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting line segments or “sides” that are joined pairwise to form a single closed path.
Is shoelace method clockwise or anticlockwise?
The method consists of cross-multiplying corresponding coordinates of the different vertices of a polygon to find its area. It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the polygon, like tying shoelaces. List all the vertices in anticlockwise order.
Does shoelace theorem work in 3D?
This research takes The Shoelace Formula (also known as Surveyor’s area formula) — a formula to find the area of a polygon in 2D (Braden, 1986) — and modified it to work in 3D. This new formula has been mathematically proven and tested with a calculation of different kinds of shapes using a computer program.
What is the area of the polygon in square units?
Area of Regular Polygons
| Names of Regular Polygon | Area of Regular Polygon |
|---|---|
| Square | Area = (length)2 |
| Regular Pentagon | Area = 5/2 × side length × length of the apothem OR Area =14×√5(5+2√5)×(side)2 1 4 × 5 ( 5 + 2 √ 5 ) × ( s i d e ) 2 |
| Regular Hexagon | Area = [3√3 ×(length of a side)2]/2 |
What is apothem in polygon?
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word “apothem” can also refer to the length of that line segment.