al. Flache (f.), Fr. Aire (f.), Eng. area. In mathematics; measure of confined, closed surfaces. The areas of many surfaces with different shapes (for example) of a circular surface and a square-shaped surface may be equal to each other.
Calculating the area of any surface; The basic principle is to divide the surface into unit surface size (areas) and determine the number of unit areas. The application of this process is very difficult, even for some large terrain, curved surfaces such as spherical surfaces, or the process may not give correct results. For this reason, formulas have been developed for calculating the areas of some geometric figures.
The unit area is a square with a unit side and it is called a unit square. It is expressed as (unit)2 by placing the number 2 on the measure symbol. Subfolders and multiples of the area unit float, shrink and grow, respectively. Subfolders of 1 m2 are:
1m2 = 100 dm2 = 10000 cm2 = 1000000 mm2.
The multiples of 1 m2 are; 1 dam2 = 100 m2, 1hm2 = 100 dam2 = 10000 m2, 1km2 = 100 hm2 = 10000 dam2 = 1000000 m2.
One method to calculate the areas of surfaces is to divide the surface into geometric shapes whose areas are known. The area of the surface divided into geometric shapes with known areas is the sum of these areas.
If any surface cannot be divided into geometric shapes whose areas can be calculated, then the area of the surface can be found by integral calculation.
f(x) ) curve is the area of the region bounded by the x-axis, x=a or x=b lines. and the area between:
can be found by calculating the integral.
Area formulas of various geometric shapes:
Triangle : A= ah/2 (h: height, a: base)
Rectangle: A=a.b (a: long side, b: short side)
Square : A = a2(a : side length)
Parallelogram : A = a.h (a: base, h: height)
Circle: A = p r2 (p : pi number, r: radius)
Ellipse : A = p .a.b (a: long radius, b: short radius)
Sphere : A = 4p r2 (p : pi number, r: radius)
Cylinder side surface: A = 2p rh (p: pi number, r: radius, h: height)