Calculation of perimeter

1.

Formula editing

1. Circle: C= π d=2 π R (D is diameter, R is radius, π)

The circumference of triangle C = a + B + C (ABC is the three sides of triangle)

3. Quadrilateral: C = a + B + C + D (ABCD is the side length of quadrilateral)

4. Rectangle: C = 2 (a + b) (a is the length, B is the width)

5. Square: C = 4A (a is the side length of square)

6. Polygon: C = the sum of all sides

The perimeter of the sector: C = 2R + n π R ÷ 180˚ ( N = center angle of circle) = 2R + Kr (k = radian)

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< H2 > the length integral around the edge of a limited area in the extended data

is called perimeter, that is, the length of a graph. The perimeter of a polygon is also equal to the sum of all the edges of the graph and the perimeter of a circle= π d=2 π R (D is diameter, R is radius, π)， Perimeter of sector = 2R + n π R ÷ 180˚ ( N = center angle) = 2R + Kr (k = radian)

For triangles of the same area, the perimeter of equilateral triangle is the shortest; If a quadrilateral of the same area is used, the perimeter of the square is the shortest; If a Pentagon of the same area is used, the perimeter of a regular pentagon is the shortest; For any polygon of the same area, the perimeter of the regular circle is the shortest. Perimeter can only be used for two-dimensional graphics (plane, surface), three-dimensional graphics (solid), such as cylinder, cone, sphere, etc. can not be expressed by the perimeter of its boundary size, but by the total surface area

total surface area = the sum of the areas of all surfaces of the solid

2.

Circumference formula of circle: circumference C of circle= π X diameter= π X radius x2 π= 3.14)

when the diameter of a circle is 50, s = 3.14x 50 = 157

a compass is usually used to draw a circle. The diameter, radius and length of the inner circle of the same circle are always the same. A circle has innumerable radii and diameters. A circle is an axisymmetric and centrosymmetric figure. The axis of symmetry is the line on which the diameter lies

The length of a circle is the circumference of a circle. Two circles that can coincide are called equal circles, and there are countless axes of symmetry. A circle is a positive n-sided shape (n is an infinitely large positive integer), whose side length is infinitely close to 0 but can never be equal to 0

extended data:

sector arc length L = center angle (radian system) × R= n π R/180 θ (R is the sector radius)

sector area s = n π R²/ 360 = LR / 2 (L is the arc length of the sector)

cone bottom radius r = NR / 360 (R is the bottom radius) (n is the center angle of the circle)

position relationship between the line and the circle:

1. The line and the circle have no common point, which is called separation. AB is separated from circle O, D & gt; r

There are two common points between a line and a circle, which are called intersection. This line is called secant of a circle. AB intersects ⊙ o, D & lt; r

3. A line and a circle have and only have one common point, which is called tangent. This line is called tangent of a circle, and the only common point is called tangent. The line between the center of the circle and the tangent point is perpendicular to the tangent line. AB is tangent to ⊙ o, d = R D is the distance from the center of the circle to the straight line)

3.

1. Formula of perimeter and area of rectangle and square:

perimeter of rectangle = (length + width) × 2 C=(a+b) × 2

perimeter of square = side length × 4 C = 4A

area of rectangle = length × Width s = AB

square area = side length × Side length s = a · a = A & # 178

Area formula of triangle, parallelogram and trapezoid:

area of triangle = bottom × high ÷ 2 S=ah ÷ 2

area of parallelogram = bottom × Height s = ah

area of trapezoid = (upper bottom + lower bottom) × high ÷ 2

S=a＋bh ÷ 2

3. Circle circumference and area formula:

circle circumference = diameter ×π

formula: l = π d＝2 π R

area of circle = radius × radius ×π

formula: S = π r²

The formula of the side area and the surface area of the cylinder:

the side area of the cylinder:

the side area of the cylinder is equal to the circumference of the bottom multiplied by the height

formula: S = Ch= π dh＝2 π RH

surface area of a cylinder:

the surface area of a cylinder is equal to the circumference of the bottom multiplied by the height, plus the area of the circles at both ends

formula: S = ch + 2S = ch + 2 π r²

extended data

1. Volume formula of cylindrical cone:

volume of cylinder:

volume of cylinder is equal to bottom area multiplied by height

The formula: v = sh

volume of cone = 1 / 3 bottom × The plot is high

formula: v = 1 / 3SH

2. Addition and subtraction rules of fractions:

addition and subtraction of fractions with the same denominator, only add and subtract the molecules, and the denominator remains unchanged

In addition and subtraction of fractions with different denominators, first pass the score, then add and subtract

3. Multiplication rule of fraction:

use the proct of molecule as molecule and the proct of denominator as denominator

Division rule of fraction:

dividing by a number is equal to multiplying by the reciprocal of the number

4.

Calculation of circumference

1. Circumference = circumference ratio × Diameter, letter formula: C= π d

2, circumference = circumference ratio × radius × 2. Letter formula: C = 2 π r

the length of the curve surrounding the circle is the circumference of the circle. The circumference of a circle depends on its diameter (radius)

PI is the ratio of circumference to diameter

in a plane, the closed curve formed by a moving point rotating one circle with a certain point as the center and a certain length as the distance is called a circle. A circle has innumerable points

in the same plane, the set of points whose distance to a fixed point is equal to a fixed length is called a circle. A circle can be expressed as a set {m | Mo | = R}. The standard equation of a circle is (x - a) & # 178; + y - b) ² = r ² Where o is the center of the circle and R is the radius

A circle is a geometric figure. By definition, a circle is usually drawn with a compass. The diameter, radius and length of the inner circle of the same circle are always the same. A circle has innumerable radii and diameters. A circle is an axisymmetric and centrosymmetric figure

The axis of symmetry is the straight line where the diameter is. At the same time, circle is a "positive infinite polygon", and "infinite" is just a concept. The more sides a polygon has, the closer its shape, perimeter and area are to a circle. Therefore, there is no real circle in the world. In fact, a circle is just a conceptual figure

a circle can be divided into several equal parts to form an approximate rectangle. The width of a rectangle is equal to the radius of a circle

5.

Circumference formula of circle:

< H2 > extended data

Properties of circle:

1. A circle is an axisymmetric figure, and its axis of symmetry is any straight line passing through the center of the circle. A circle is also a centrosymmetric figure, and its center of symmetry is the center of the circle

Vertical diameter theorem: bisect the chord perpendicular to the diameter of the chord, and bisect the two arcs of the chord

The inverse theorem of the vertical diameter theorem: the diameter of bisector string (not diameter) is perpendicular to the string, and bisector the two arcs of the string

The properties and theorems of the angle of circle circumference and the angle of circle center

in the same circle or equal circle, if one of the two central angles, two peripheral angles, two groups of arcs, two strings and the distance between the centers of two strings is equal, then the other corresponding groups are equal

in the same circle or equal circle, the circumference angle of the equal arc is equal to half of the center angle of the circle it is opposite (the circumference angle and the center angle are on the same side of the chord)

The degree of the tangent angle is equal to half of the degree of the arc

The degree of the inner angle of the circle is equal to half of the sum of the degrees of the arc to which the angle is directed

The degree of the outer angle of the circle is equal to half of the difference between the degrees of the two arcs cut by the angle

The area of circle is larger than that of square, rectangle and triangle

6.

C=2 π r

C= π D

(1) a circle is an axisymmetric figure, and its axis of symmetry is any straight line passing through the center of the circle. A circle is also a centrosymmetric figure, and its center of symmetry is the center of the circle

Vertical diameter theorem: bisect the chord perpendicular to the diameter of the chord, and bisect the two arcs of the chord. Inverse theorem: bisecting the diameter of the string (not the diameter) is perpendicular to the string, and bisecting the two arcs of the string

In the same circle or equal circle, if one of the two central angles, two circular angles, two groups of arcs, two strings and the distance between the centers of two strings is equal, then the other groups of quantities corresponding to them are equal

(2) the circular angle of an arc is equal to half of the central angle of the circle

The circumference angle of

diameter is right angle. A circle angle of 90 degrees is the diameter of the chord

The formula for calculating the center angle of a circle is as follows: θ=( L/2 π r) × three hundred and sixty °= one hundred and eighty ° L/ π R = L / R (radian) (angle system and radian system: 360) °= two π

In other words, the degree of the central angle of a circle is equal to the degree of the arc it faces; The degree of a circular angle is equal to half of the degree of the arc it faces

(3) if the length of an arc is twice that of the other arc, the circle angle and center angle of the opposite arc are twice that of the other arc

(3) the properties and theorems of circumscribed circle and inscribed circle (1) a triangle has a unique circumscribed circle (∵ three points determine a circle)

circle and inscribed circle. The center of the circumscribed circle is the intersection of the vertical bisectors of each side of the triangle, and the distance to the three vertices of the triangle is equal

(2) the center of the inscribed circle is the intersection of the bisectors of the internal angles of the triangle, and the distance from the center to the three sides of the triangle is equal

③R=2S△ ÷ L (R: radius of inscribed circle, s △: area of triangle, l: perimeter of triangle)

④ the connecting center line of two tangent circles passes through the tangent point (connecting center line: straight line connecting two centers)

⑤ the midpoint m of chord PQ in circle O, and the crossing point m is the midpoint m of XY if two strings AB, CD, ad and BC intersect PQ at x and Y respectively

(4) if two circles intersect, the line segment connecting the centers of the two circles (or the line) vertically bisects the common chord

(5) the degree of the chord tangent angle is equal to half of the degree of the arc it contains

(6) the degree of the inner angle of a circle is equal to half of the sum of the degrees of the arc to which the angle is directed

(7) the degree of the outer angle of the circle is equal to half of the difference between the degrees of the two arcs cut by the angle

The area of circle is larger than that of rectangle, square and triangle

extended data

the ratio of the circumference of any circle to its diameter is a fixed number. We call it pi, which is expressed in letters π PAI). It is an infinite acyclic decimal (irrational number), π= 3.1415926535897... But in practical application, only its approximate value is generally taken, i.e π If C is used to represent the circumference of a circle: C= π D or C = 2 π r. On Zhoubi Suanjing; Wednesday is Monday;, Take Pi as 3, but this is only an approximation

When Mesopotamians made the first wheel, they only knew that the PI was 3. In 263 ad, Liu Hui of the Wei and Jin Dynasties annotated nine chapters of arithmetic; Wednesday, Monday & quot; It's just the ratio of circumference to diameter of a regular hexagon inscribed in a circle. He founded the circle cutting technique. He thought that when the number of sides of a regular polygon in a circle increased infinitely, the perimeter of the circle would be closer to the perimeter of the circle

he calculated the circumference of the square 3072 inscribed in the circle, π= 3927/1250 Liu Hui applied the concept of limit to solve practical mathematical problems, which is also a great achievement in the history of world mathematics. In 1500 years ago, Zu Chong (429-500 AD) continued to calculate on the basis of previous calculations, and found that the PI was between 3.1415926 and 3.1415927, which was the earliest seven decimal accurate value in the world, about 1000 years earlier than Europe. He also used two fractional values to express the PI: 22 / 7 is called approximate ratio, 355 / 113 is called density ratio

In Europe, it was not until the 16th century, 1000 years later, that the German ETU (1573 A.D.) and antoniz got this value. Now with computers, the PI has reached hundreds of millions of decimal places

7.

The so-called circumference of a cylinder refers to the circumference of the bottom (section) of the cylinder

If the circumference of the bottom surface of the

cylinder is a circle, then the circumference of the

circle = Pi × Diameter

C= π D

circumference of circle = circumference ratio × two × Radius
C = 2 π R

there is a fixed line and a moving line in the same plane. When the plane rotates around the fixed line, the surface formed by the moving line is called the rotating surface, the fixed line is called the axis of the rotating surface, and the moving line is called the generatrix of the rotating surface. If the generatrix is a straight line parallel to the axis, the resulting surface of rotation is called a cylindrical surface

If two planes perpendicular to the axis are used to truncate the cylindrical surface, then the geometry enclosed by the two sections and the cylindrical surface is called a straight cylinder

1. Take the line on one side of the rectangle as the axis of rotation, and the surface formed by the rotation of the other three sides is called a circular cylinder, that is, one side of the Ag rectangle is the axis and rotates 360 degrees ° The resulting geometry is a cylinder

where AG is called the axis of the cylinder, the length of Ag is called the height of the cylinder, and all lines parallel to Ag are called the generatrix of the cylinder, DA and D & #; The two circles formed by the rotation of G are called the bottom of the cylinder, DD & # 39; The surface formed by rotation is called the side of a cylinder

2. There is a fixed line and a moving line in the same plane. When the plane rotates around the fixed line, the surface formed by the moving line is called the rotating surface, the fixed line is called the axis of the rotating surface, and the moving line is called the generatrix of the rotating surface. If the generatrix is a straight line parallel to the axis, the resulting surface of rotation is called a cylindrical surface

If two planes perpendicular to the axis are used to cut the cylindrical surface, then the geometry enclosed by the two sections and the cylindrical surface is called a straight cylinder

In the same plane, there is a fixed line and a moving line. When the plane rotates around the fixed line for one circle, the surface formed by the moving line is called the rotating surface, the fixed line is called the axis of the rotating surface, and the moving line is called the generatrix of the rotating surface. If the generatrix is a straight line parallel to the axis, the resulting surface of rotation is called a cylindrical surface

If two planes perpendicular to the axis are used to cut the cylindrical surface, then the geometry enclosed by the two sections and the cylindrical surface is called a straight cylinder

8.

Algorithm: perimeter = side length × 10

principle: each side of a five pointed star is equal. There are ten sides in a five pointed star, and the perimeter is the sum of all sides, so the perimeter = side length × 10

The five vertices of the regular Pentagram are evenly distributed on the circle

The five-star red flag is the national flag of the people's Republic of China stipulated in the constitution of the people's Republic of China. Red symbolizes revolution; The five stars are yellow, which symbolizes that Chinese people are yellow

big stars represent the Communist Party of China and small stars represent workers, peasants, intellectuals and national bourgeoisie

the four small stars arch on the right of the big star, and each has a sharp corner facing the center of the big star, which symbolizes the great unity of the revolutionary people and the support of the people for the party under the leadership of the Communist Party of China

9.

Circumference of circle: C = 2 π r= π D (R is the radius and D is the diameter)

Calculation formula of area of a circle:

extended data:

Properties of a circle

(1) a circle is an axisymmetric figure, and its axis of symmetry is any straight line passing through the center of the circle. A circle is also a centrosymmetric figure, and its center of symmetry is the center of the circle

Vertical diameter theorem: bisect the chord perpendicular to the diameter of the chord, and bisect the two arcs of the chord

The inverse theorem of the vertical diameter theorem: the diameter of bisector string (not diameter) is perpendicular to the string, and bisector the two arcs of the string

In the same circle or equal circle, if one of the two central angles, two circular angles, two groups of arcs, two strings and the distance between the centers of two strings is equal, then the other groups of quantities corresponding to them are equal

(2) in the same circle or equal circle, the circumference angle of the equal arc is equal to half of the center angle of the circle (the circumference angle and the center angle are on the same side of the chord)

The circumference angle of

diameter is right angle. A circle angle of 90 degrees is the diameter of the chord

The formula for calculating the center angle of a circle is as follows: θ=( L/2 π r) × three hundred and sixty °= one hundred and eighty ° L/ π R = L / R (radians)

In other words, the degree of the central angle of a circle is equal to the degree of the arc it faces; The degree of a circular angle is equal to half of the degree of the arc it faces

(3) if the length of an arc is twice that of the other arc, the circle angle and center angle of the opposite arc are twice that of the other arc

(3) properties and theorems of circumscribed circle and inscribed circle (1) a triangle has a unique circumscribed circle and inscribed circle. The center of the circumscribed circle is the intersection of the vertical bisectors of each side of the triangle, and the distance to the three vertices of the triangle is equal

(2) the center of the inscribed circle is the intersection of the bisectors of the internal angles of the triangle, and the distance from the center to the three sides of the triangle is equal

③R=2S△ ÷ L (R: radius of inscribed circle, s: area of triangle, l: perimeter of triangle)

(4) the connecting line of two-phase tangent circle passes through the tangent point Connecting center line: a straight line connecting the centers of two circles)

⑤ the midpoint m of the chord PQ in the circle O. if passing through the point m, any two strings AB, CD, AC and BD intersect PQ at x and Y respectively, then M is the midpoint of XY

(4) if two circles intersect, the line segment connecting the centers of the two circles (or the line) vertically bisects the common chord

(5) the degree of the chord tangent angle is equal to half of the degree of the arc it contains

(6) the degree of the inner angle of a circle is equal to half of the sum of the degrees of the arc to which the angle is directed

(7) the degree of the outer angle of the circle is equal to half of the difference between the degrees of the two arcs cut by the angle

The area of circle is larger than that of square, rectangle and triangle