Mathematical Trapezoidal Formulas What are all the formulas for trapezoids?

The circumference formula of the trapezoid: if the upper bottom of the trapezoid is A, the lower bottom is B, the two waist lengths are C and D respectively, and the circumference is L, then the perimeter formula of the trapezoid is: L=A+B+C+D, which is popularly expressed as:

Upper bottom + lower bottom + waist + waist.

The circumference formula of the isosceles trapezoid: Since the two waists of the isosceles trapezoid are equal in length, that is, c = d, the perimeter formula of the isosceles trapezoid can be simplified as: l = a + b + c + d = a + b + 2c = a + b + 2d, which is popularly expressed as:

Upper bottom + lower bottom + 2 waist.

The perimeter and area of the trapezoid.

The area formula of the trapezoid: the area formula of the trapezoid: let the upper bottom length of the trapezoid be a, the lower bottom length is b, the height is h, and the area is s, then the trapezoidal area formula is s=(a+b) h 2, which is popularly expressed as:

Upper bottom + lower bottom) High 2.

Special Case:

1. If the median length of the trapezoid is known to be l, according to the above trapezoidal property 2, the trapezoidal area formula is: s=l h;

2. If the two diagonals of the trapezoid are perpendicular to each other and the lengths are x and y respectively, then the trapezoidal area formula is s=xy 2;

3. If the length of the bottom and waist of the trapezoid is known, and the length of the height is unknown, the formula for the area of the trapezoid is:

s=［（a+c）/4（a-c）］×a+b-c+d）（a-b-c+d）（a+b-c-d）（-a+b+c+d）］

The formula for calculating the trapezoid is the area of the trapezoid = (upper bottom + lower bottom) * height 2. A trapezoid is a quadrilateral with only one set of opposite sides parallel. The two parallel sides are called the bottom edge of the trapezoid:

The longer bottom edge is called the bottom bottom, and the shorter bottom edge is called the bottom bottom; The other two sides are called the waist; The perpendicular segment sandwiched between the two bases is called trapezoidal height. A trapezoid with a waist perpendicular to the bottom is called a right-angled trapezoid. A trapezoid with two equal waists is called an isosceles trapezoid.

A group of quadrilaterals where the opposite sides are parallel and the other is not parallel to the opposite sides is a trapezoid. A group of quadrilaterals with parallel and unequal opposite sides is trapezoidal.

The trapezoid only has an area formula, and the perimeter formula is the upper bottom + lower bottom + two waist lengths.

Hope it helps!

1. The trapezoidal circumference formula c = upper bottom + lower bottom + two waist lengths.

2. Isosceles trapezoid.

The circumference formula: upper bottom + lower bottom + 2 waist.

3. Trapezoidal area formula.

s=1 2 (top bottom + bottom bottom) * high.

4. The area formula of the trapezoid: median line.

High. 5. Diagonal.

The area of the trapezoids perpendicular to each other is: diagonal Diagonal 2

Quality. 1 The two waists of an isosceles trapezoid are equal.

2 The two base angles of the isosceles trapezoidal on the same base are equal.

3 The two diagonals of an isosceles trapezoidal are equal.

4 Isosceles trapezoids are axisymmetric figures.

The axis of symmetry is the straight line where the line connecting the midpoints of the upper and lower bases is located (the straight line that crosses the midpoints of the two bases).

Decide. A trapezoid with two equal waists is an isosceles trapezoid;

A trapezoid with two equal angles on the same base is an isosceles trapezoid;

A trapezoid with equal diagonal lines is an isosceles trapezoid.

Let the length of the upper edge of the right-angled trapezoid be a, the length of the lower edge be b, and the height of the right angle trapezoid be h, then:

1. The height of its center of gravity from the lower bottom edge b is: <

2. The distance between its center of gravity and the right-angled side is: <

In a right-angled trapezoidal ABCD, AD BC, B=90°, then A=90°, C+ D=180°.

Important properties: The distance from the midpoint of the right-angled trapezoidal oblique waist to the two ends of the right-angled waist is equal.

1. The trapezoidal circumference formula c = upper bottom + lower bottom + two waist lengths.

2. The circumference formula of isosceles trapezoid: upper bottom + lower bottom + 2 waist.

3. Trapezoidal area formula: s=1 2 (upper bottom + lower bottom) * high.

4. The area formula of the trapezoid: the median line is high.

5. The trapezoidal area perpendicular to each other is: diagonal 2<>

1. The area formula of the trapezoid: (upper bottom + lower bottom) height 2

The area of the trapezoid is equal to half of the product of the sum of the upper and lower bases and the height. If the upper and lower bases of the trapezoid are represented by a and b respectively, and the height is represented by h, the area of the trapezoid is s=(a+b) h2.

2. The area formula of the trapezoid: the median line is high.

According to the length of the median line of the trapezoid, which is equal to half of the sum of the upper and lower bases, the area of the trapezoid is also equal to the product of the median line and the height. If the median line of the trapezoid is denoted by m and the height is denoted by h, the area of the trapezoid is s=mh.

3. The area of the ladder closed old shape perpendicular to each other is: diagonal diagonal 2.

The two waists of the waist trapezoid are equal, the two elementary base angles of the isosceles trapezoid on the same base are equal, the two diagonals of the isosceles trapezoid are equal, the isosceles trapezoid is an axisymmetric figure, and the axis of symmetry is the straight line where the line connecting the midpoint of the upper and lower bases is located.

Expansion of the car and the exhibition information:

To determine that an arbitrary quadrilateral is an isosceles trapezoid, if the determination theorem of the isosceles trapezoidal cannot be directly applied, the general method is to decompose the quadrilateral into a familiar polygon by making auxiliary lines, in this case by making parallel lines, decomposing the quadrilateral into a parallelogram and an isosceles triangle.

Make a diagonal parallel line over the vertex, concentrate the quantitative relationship and position relationship of the two diagonals into a triangle, and convert the length of the upper and lower bottom of the trapezoid into the length of the hypotenuse of the right triangle.

The upper and lower bottom edges of the trapezoid are parallel, the height of both sides is equal, both are h, the square of the length of the hypotenuse = the square of the height + the square of (the bottom of the bottom - the bottom of the top) (assuming that the bottom bottom is longer than the length of the top bottom) In other words: the length and height of the part of the bottom that is more than the bottom are two right-angled sides, and the trapezoidal hypotenuse is the hypotenuse of a triangle, and these three lines form a right-angled triangle.

The above formula is the Pythagorean theorem of a right triangle.

Obtained by using the above formula, you can find the hypotenuse: the length of the hypotenuse = (h?+(l down - l up)?)

The calculation of the trapezoidal funnel is the calculation of the triangular pyramid, and the volume is one-third of the volume of the cylinder of the same height as the bottom area, and the volume of the cylinder is the base area multiplied by the height.

Divide the trapezoid into two triangles and a rectangle, calculated using the Pythagorean theorem or using the sine and cosine theorem.

Perimeter formula for trapezoid:

1) The circumference formula of the trapezoid: upper bottom + lower bottom + waist + waist.

2. The circumference formula of isosceles trapezoid: upper bottom + lower bottom + 2 waist.

Area formula for trapezoid:

1) The area formula of the trapezoid: (upper bottom + lower bottom) High 2, represented by letters:

Deformation: h=2s (a+c); Deformation 2: a=2s h-c; Deformation 3: c = 2s h-a. (S area, A top bottom, C bottom bottom, H height).

2) The area formula of the trapezoid: median line high, represented by letters: l·h.

3) The trapezoidal area perpendicular to each other is: diagonal, diagonal 2.

Area formula for fractional trapezoid:

The formula for the area of the fractional trapezoid: (upper base + lower bottom) high 2, represented by letters: s=(a+b) h 2.

Deformation 1: h=2s (a+b); Deformation 2: a=2s h-b; Deformation 3: b = 2s h-a.

Another formula for calculating the area of a trapezoid: median line height, represented by letters: l·h.

The area of the trapezoidal where the diagonals are perpendicular to each other is: diagonal diagonal 2.

Trapezoidal area = (upper bottom + lower bottom) height 2

Represented by letters: s=(a+b) h2

The trapezoidal area formula (top bottom + bottom bottom) x height 2

The area of the trapezoid = (upper bottom + lower bottom) x height 2

The formula for calculating the area of a trapezoid is (upper bottom + lower bottom) height 2

The formula for calculating the trapezoid is as follows:

1. The formula for calculating the circumference of the trapezoid: circumference = upper bottom + lower bottom + waist + waist.

It is represented by letters: L=A+B+C+D (let the length of the upper bottom be A, the length of the lower bottom is B, the length of the two waists is C, D, and the circumference is L).

2. The formula for calculating the circumference of an isosceles trapezoid: circumference = upper bottom + lower bottom + 2 waist.

Represented by letters: L=A+B+2D (Let the length of the upper bottom be A, the length of the lower bottom is B, the length of the two waists is C, D, and the circumference is L, due to the isosceles trapezoidal.)

The length of the two waists is equal, that is, C = D, simplification can obtain L = A + B + 2D) 3, the area formula of the trapezoid: area = (upper bottom + lower bottom) High 2 is represented by letters: s = (a + b) * h 2 (let the upper bottom length of the trapezoid be a, the lower bottom length is b, the height is h, and the area is s).