Questions about the relationship between the length, area, and perimeter of the three sides of a tri

Triangle area formula.

Area = base height 2, s = ah 2 (where a is the bottom of the triangle, do hh is the height corresponding to the bottom).

Note: All three sides can be the base, which should be understood as half of the high product corresponding to the three sides is the area of the triangle.

So: base = triangle area multiplied by 2 divided by high, i.e. a = 2s h

Triangle circumference: If the three sides of a triangle are a, b, and c, then the perimeter c=a+b+c

The important four lines of the triangle:

Midline. The line segment that connects a vertex of a Gorhuyan triangle to the midpoint of its opposite side is called the midline of the triangle.

median）。

High. Draw a perpendicular line from a vertex to the line where its opposite edge is located, and the line segment between the vertex and the perpendicular foot is called the altitude of the triangle.

Angular bisector. The bisector of an inner corner of a triangle intersects the opposite side of the angle, and the line segment between the vertices and the intersection of the corner is called the bisector of angle.

Median line. The line connecting the midpoints of any two of the three sides of the triangle is called the median line. It is parallel to the third side and equal to one and a half of the third side.

a. After the length of each side of the triangle is determined, the circumference and area of the ruler are determined, which is correct, because the triangle has a stable trace qualitative, and the three sides are determined, the perimeter is certain, and the area is certain;

b. After the length of each side of the parallelogram is determined, the perimeter and area are determined, which is wrong, because the length of the four sides has not changed, so the perimeter has not changed, but the height has changed, so the area has changed;

c. After the radius of the circle is determined, according to the circumference of the circle = 2 r and the area of the circle = r2, it can be known that the perimeter and area are determined, so the statement is correct;

Therefore, b

Let the side length of the equilateral triangle be a, the perimeter of the triangle = 3a, the area of the triangle = 1 Lingxian 2 a 3 2 a = 3 4 a, the area of the triangle The perimeter of the triangle = ( crack 3 4 a ) 3a) = 3 12 a, the relationship is: the ratio of the area of the equilateral triangle to the perimeter is 3 12 times the side length.

The formula for the area of an equilateral triangle is:

s=( 3)A 4,(s is the area of the triangle, A is the length of the side of the triangle)1, the formula for the area of the triangle is: s=(1 2)ah (s is the area of the triangle, a is one side of the triangle, h is the height of this side).

2. In a regular triangle, the three sides are equal, and the height on the three sides also corresponds to the same, the side length is blind a, and the height is h, then h=(3)a 2

Therefore, it can be deduced that the area of a regular triangle s=(1 2)ah=(3)a 4 equilateral triangle (also known as a regular trilateral) is a triangle with three equal sides, and its three internal angles are equal, all of which are 60°, which is a kind of acute triangle. Equilateral triangles are also the most stable structure. Equilateral triangles are special isosceles triangles, so equilateral triangles have all the properties of isosceles triangles.

The conditions are not enough. The circle is inlaid with a quadrilateral: s = (p-a) (p-b) (p-c) (p-d) where p = (a+b+c+d) 2

Arbitrary quadrilateral:

1.If the four sides of the quadrilateral are a, b, c, d, and the two opposite diagonals are , then p=(a+b+c+d) 2; = 2, area s = (p-a) (p-b) (p-c) (p-d)-abcd cos

2.If the two diagonals of the four-sided ruler shape are p and q respectively, the middle angle of the two high diagonals of the reed cover is , and the area is 2s=pq sin

The circumference of the triangle is equal to the sum of the lengths of the three sides of the triangle.

Perimeter: The integral of the length of the edge of the area around a finite area, denoted by the letter c, and the length of the perimeter of the polygon is equal to the sum of all sides of the figure.

A triangle is a closed figure composed of three line segments in the same plane that are not on the same straight line in order to end, which has applications in mathematics and architecture.

Common triangles are divided into ordinary triangles according to sides, isosceles triangles, right triangles, acute triangles, obtuse triangles, etc., among which acute triangles and obtuse triangles are collectively referred to as oblique triangles.

The side length of the triangle is denoted as a, b, c, and its perimeter is a+b+c. You ask for a side length. The other is the relationship between the side lengths of the triangles.