How a triangle derives the circular area formula

First, divide the circle into n small sectors, when the central angle of each small sector.

At very small ages, the sector is similar to an isosceles triangle.

The area of the triangle is one-half of the base times the height, and the base is approximately the length of the sector arc.

High myopia. The radius of the circle, s fan s l*r 2, n sector area.

The sum of is the circle.

s circle = nlr 2 = (2 r) r 2 = r(This is the limit of the sum of infinite divisions).

1. Circle area: s= r, s= (d 2). d is the diameter, r is the radius).

2. The area of the semicircle.

s semicircle = (r 2) 2. (r is the radius).

3. The area of the circle: S large circle - S small circle = (r 2-r 2) (r is the radius of the large circle, r is the radius of the small circle).

4. The circumference of the circle: c=2 r or c=d. d is the diameter, r is the radius).

5. The circumference of the semicircle: d+(d) 2 or d+ r. d is the diameter, r is the radius).

6. The area of the circle where the fan is located is divided by 360 and multiplied by the angle n of the central angle of the fan, as follows:

s=n/360×πr²

s= r l 2 r = lr 2 (l is the arc length, r is the fan radius).

Draw a number of straight lines through the center of the circle by the cutting method, divide the circle into a number of fans, and when there are many straight lines, the fans are approximately triangular. The area of the triangle is 2 at the base * height. The area of the circle is equal to the sum of the areas of the triangles (e.g., n), i.e. = n * base * height 2

Because n*bottom = circumference of the circle = 2 * radius, the radius of the circle.

So the area of the circle = 2 * radius * radius 2 = square of the radius *

First of all, the circle is evenly divided into a number of fans, each sector is like a small triangle, the arc length of the fan is equivalent to the bottom of the triangle, and the radius is equivalent to the height of the triangle, so that the area of the fan can be used

Sector area = arc length radius 2

So, the area of the circle = the circumference of the circle and the radius 2= r.

1. The area of the semicircle: s semicircle = (r 2) 2. (r is the radius).

2. The area of the ring: S big circle - S small circle = (r 2-r 2) (r is the radius of the large circle, r is the radius of the small circle).

3. The circumference of the circle: c=2 r or c=d. d is the diameter, r is the radius).

4. The circumference of the semicircle: d+(d) 2 or d+ r. d is the diameter, r is the radius).

5. The arc length of the sector l=the central angle (radian) r= n r 180 (the central angle) (r is the radius of the fan).

6. The sector area s=n r 360=lr 2 (l is the arc length of the fan).

7. The radius of the bottom surface of the cone r=nr 360 (r is the radius of the bottom surface) (n is the central angle).

is the sum of an infinite number of small sector areas, so in the last formula, the sum of the small arcs of the segments is the circumference of the circle 2 r, so there is s = r.

Divide the circle into many small triangles with the center of the circle as the vertex and the arc as the bottom edge.

The height of each small triangle is the radius.

The area of each small triangle = 1 2 * base * height.

Circle area = area of all small triangles.

Sum = 1 2 * height (sum of base edges) = 1 2 * radius * circumference.

1/2*r*2πr=πr²。

Brief introduction. Area is the number of degrees that represent a two-dimensional figure or shape or plane layer in a plane. Surface area.

is a simulant on a two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness, the area is necessary to form a model of shape, or the amount of paint required to cover a surface with a single coat. It is a two-dimensional simulation of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

Summary. Hello, it is a pleasure to help you with your studies.

To derive the formula of a circle using the area formula of a triangle, it is necessary to divide the circle into multiple small sectors. Reuse the formula of the triangle to derive it.

How to derive the area formula of a circle using the area formula of a triangle.

Hello, it is a pleasure to help you with your studies. Using the area formula of the triangle to derive the formula of the circle of the Yan Song, it is necessary to divide the circle into multiple small fan-shaped jujube skins. Reuse the formula of the triangle to derive it.

The data you gave needs to be graphically corresponding. It is best to provide graphics in order to answer more accurately

It is to divide a circle into many, many small triangles for infinite division, that is, to infinitely close the circumference of the triangle to the bottom of the triangle.

In this way, it can be directly understood that the bottom of the triangular celery shape is the circumference of the circle. The height is the radius of the circle. Then the area of the triangle is equal to the base multiplied height divided by two.

s=ah 2=cr 2=2 I hope you will refer to it carefully. I also hope that mine will help you, and I wish you all the best in your learning and progress

Therefore, there is no direct connection between what you have just expressed above. You will calculate the area of the triangle as the area of the circle. to find the diameter of the circle.

A polyline is used to close any triangle into a circle.

The area of a trapezoid, rectangle, or regular n-sided shape is used to derive the area of a circle.

The formula is unattainable. Because the circle is not made according to the area of a triangle, trapezoid, rectangle, or regular n-sided shape.

Because the area of any known circle buried by Kuansun is softened and deformed by equal area is seven-ninths of the area of its own inscribed square, "the area of the circle."

s is equal to seven times the square of one-third of its diameter d". The formula for the area of a circle: s=7(d3).

The formula for the area of the triangle inside the circle: the area of the triangle = the sum of the lengths of the sides of the triangle multiplied by half of the product of the radius of the inscribed circle, half of the circumference = the area divided by the radius of the inscribed circle.

If there are three non-overlapping points a, b, and c on Sun Ranmeng's circle o, then the abc formed by these three points is called the inscribed triangle of the circle o.

The circumscribed circle of a triangle is the intersection of the perpendicular bisector of each side of the triangle, which is the outer center. The distance from the outer center to the vertices of the triangle is equal. The perpendicular line from the outer center to each side of the triangle bisects each side.

In a triangle, the inscribed circle of the bridge is the intersection of the bisector of the inner angles of the triangle, which is the heart. The distance from the heart to each side of the triangle is equal.

The two tangents of either vertex of the triangle to the inscribed circle are of equal length.

The tangent length from the vertex of the triangle to the inscribed circle is the mid-term between the distance from this point to the center of the circle and the outer part of the circle.

Set the triangle. If the radius of the abc circumscribed sleek is r, then the source chain.

s triangle abc = (1 hail let sun 2) absinc = 2r 2sinasinbsinc

Draw a number of straight lines through the center of the circle by the cutting method, divide the circle into a number of fans, and when there are many straight lines, the fans are approximately triangular. The area of the triangle is the base * height of Hail 2The area of the circle is equal to the sum of the areas of the triangles (e.g., n), i.e. = n * base * height 2

Because n*bottom = circumference of the circle = 2 * radius, the radius of the circle.

So the circle refers to the area of the implicit = 2 * radius * radius 2 = square of the radius *

Draw a number of straight lines through the center of the circle, divide the circle into several fans, and when there are many straight lines, the fan shape is similar to a triangle. The area of the triangular shirt pie is the bottom * height 2The area of the circle is equal to the sum of the areas of the triangles (e.g., n), i.e. = n * base * height 2

Because n*base = circumference of a circle = 2 * radius or monoga, the height of a triangle = the radius of a circle.

So the area of the circle = 2 * radius * radius 2 = square of the radius *