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Perimeter Definition

A perimeter is a path that encompasses or surrounds a two-dimensional shape. The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The term may be used either for the path, or its length in one dimension. It can be thought of as the length of the outline of a shape. For a polygon, the perimeter is the sum of the lengths of the sides. The perimeter of a circle or ellipse is called its circumference although that term is used by some authors to refer to the perimeter of an arbitrary curved geometric figure.

Overview

Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter. If the length of the string was exact, it would equal the perimeter.

Perimeter & Area Formulas:

Volume formulas for various figures including lateral surface area, area of base(s), and total surface area:

Geometric Shape

Perimeter Formula

Area Formula

Symbols

Rectangle

P = 2l + 2w

A = lw

l = length, w = width.

Square

P = 4a

A = a2

a = length of a side.

Triangle

P = a + b + c

A = 12bh

a, b, c = side lengths of the triangle. b = base of triangle, h = height of triangle.

Parallelogram

P = 2b + 2h

A = bh

b = base, h = height.

Trapezoid

P = a + b + c + d

A = 12(a + b)h

a, b, c, d = sides of trapezoid. a, b = two bases, h = vertical height.

Ellipse

P = 2π√ (a22 + b22

A = πab

a = radius of the major axis, b = radius of the minor axis.

Kite

P = 2a + 2b

A = 12d1d2

a = length of the first pair of equal sides, b = length of the second pair of equal sides. d1 = long diagonal of kite, d2 = short diagonal of kite.

Rhombus

P = 4a

A = 12d1d2

a = length of a side. d1 = length of a diagonal, d2 = length of the other diagonal.

Pentagon

P = 5a

A = 52sa

a = length of a side. s = side of the pentagon, a = apothem length.

Hexagon

P = 6a

A = 3 3 2a2

a = length of a side.

Heptagon

P = 7a

A = pa2

a = length of a side. p = perimeter value, a = apothem length.

Octagon

P = 8a

A = 2a2(1 + √ 2 )

a = length of a side.

Related Definitions

Sources

“Perimeter.” Wikipedia, Wikimedia Foundation, 31 Mar. 2020, en.wikipedia.org/wiki/Perimeter.

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