Perimeter
Perimeter is the measurement that defines the distance around a two-dimensional shape, such as squares, circles, and rectangles. It represents both the distance enclosing the shape and the path formed by its edges. Understanding perimeter is practical for various applications, such as determining the amount of fencing required to enclose a garden or the fabric needed to tailor clothing. It is important to note that the relationship between perimeter and surface area can be confusing; while increasing the area generally increases the perimeter, the two measurements are not directly correlated.
To calculate the perimeter of basic shapes, different formulas apply: for a square, multiply the length of one side by four; for a triangle, sum the lengths of all three sides; for a rectangle, use the formula 2(length + width); and for equilateral polygons, multiply the number of sides by the length of one side. Notably, the perimeter of a circle, referred to as circumference, can be calculated using formulas based on the radius or diameter, utilizing the mathematical constant π (approximately 3.14). This understanding of perimeter is essential in both academic and practical contexts.
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Perimeter
Perimeter is a measurement used to describe the distance around a two-dimensional shape such as a square, circle or rectangle. It can be used to refer to either the distance around the shape or the path formed by the edges of the shape. Perimeter as a quantity is often of interest even to those other than mathematicians, because it can be used to determine how long of a fence will be needed to enclose an area, how much fabric will be needed to create a garment, and many other practical applications. Contrary to popular misconception, there is not a direct relationship between the perimeter of a shape and the total surface area of that shape, although it is true that increasing the surface area of the shape will cause the perimeter to increase as well, and decreasing the area of the shape will cause the perimeter to reduce in size. Many students of mathematics become confused at first by the relationship between area and perimeter, because of the similarity in the operations used to calculate each quantity. To find perimeter one adds together the lengths of the sides of most sided shapes involves multiplying the lengths of the sides together.
Overview
There are many different formulas used to calculate the perimeter of basic shapes. For a square, the perimeter can be found by multiplying the length of a side s by 4, since all four sides of a square have the same length. For a triangle, given sides that have lengths of a, b and c, the perimeter may be found by adding the three values together: a + b + c. Rectangles, in which opposite sides have equal lengths, require the use of the formula 2l + 2w to find the perimeter, where l is equal to the length of one of the longer sides and w is equal to the length of one of the shorter sides. Equilateral polygons, which are similar to squares in the sense that all of their sides are of equal length, have perimeters that are equal to n × a, where n is the number of sides the equilateral polygon possesses and a is the length of one of those sides.
Thus, in the case of a twelve-sided equilateral polygon with sides that are 4 inches in length, the perimeter of the equilateral polygon would be found by calculating 12 × 4, for a result of 48 inches. For a circle, the perimeter is referred to as the circumference (meaning, the distance around) and it can be calculated if one knows the radius or diameter of the circle, using either the formula 2πr (where r is the length of the radius of the circle) or πd (where d is the diameter of the circle). This is possible because the figure of a circle has a proportional relationship between its perimeter and its radius, and that proportional relationship is expressed by the constant, π, which is usually approximated by the value 3.14.
Bibliography
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