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In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is T = b h / 2 , {\displaystyle T=bh/2,} where b is the length of the base of the triangle, and h is the height or altitude of the triangle.
If a region is not convex, a "dent" in its boundary can be "flipped" to increase the area of the region while keeping the perimeter unchanged. An elongated shape can be made more round while keeping its perimeter fixed and increasing its area. The classical isoperimetric problem dates back to antiquity. [2]
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter. The solution is intuitive; it is the circle. In particular, this can be used to explain why drops of fat on a broth surface are circular. This problem may seem simple, but its mathematical proof requires some sophisticated theorems.
The largest possible ratio of the area of the inscribed square to the area of the triangle is 1/2, which occurs when =, = /, and the altitude of the triangle from the base of length is equal to . The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is 2 2 / 3 {\displaystyle 2 ...
Related: Deal or No Deal Island star Dr. Will Kirby reacts to being immediately disliked. Let’s get into what went down in the Temple, which was even more bizarre. You present Will with his ...
For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. [5] For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.
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