The waist length of the isosceles trapezoidal is 12cm, the length of the upper bottom is 15cm, and t

The bottom is 27cm. Make the auxiliary line first, and make the auxiliary line from the leftmost and rightmost bottom of the top bottom vertically. The result is 2 right triangles and 1 rectangle.

Because the angle between the top and bottom and the waist is 120°, and this angle is divided into 2 corners by the auxiliary line, the angle on the rectangle side is 90°, and the angle on the side of the triangle is 30°, and this triangle is a 30° right triangle, the side opposite by 30° is half of the hypotenuse, and the hypotenuse is the waist length of the trapezoid. So the base length of the triangle is 6cm. Because it is an isosceles trapezoid, the bottom of the triangle is 6cm in addition, too.

The opposite sides of the rectangle are equal, so the top bottom is 15cm long. Therefore, the bottom of this trapezoid is 6 + 6 + 15 = 27

The sum of the inner angles of the same side is equal to 180°, so knowing the angle between the upper bottom and the waist, you can calculate the angle between the lower bottom and the waist, in the right triangle, the hypotenuse is equal to 12cm, and the large angle is 60°, and the short right-angled side is equal to half of the hypotenuse, that is, 6cm, according to the principle of symmetry, the bottom edge is equal to 15 + 6 + 6 = --b

c e f d

That is, ab = 15cm, corresponding to ef = 15cm, angle bac and angle c are the same internal angles, complementary, angle c = 60°, ce = 1 2 * ac = 6cm, from the symmetry, fd = ce = 6cm.

Because the upper and lower bases of the isosceles trapezoid are parallel, the angle between the upper bottom and the desired plus the lower bottom angle = 180°

Make a straight line perpendicular to the bottom through the intersection of the upper bottom and the desired bottom, you can get a 30° 60° right triangle, sin30=x 12=1 2, x=6

Therefore, the length of the bottom is 15 + 6 * 2 = 27cm

Go past the vertex of the top bottom and make a waist parallel line to get a flat quadrilateral and an equilateral triangle.

The two sides of a parallelogram are 5 and 6 long, and the sides of an equilateral triangle are 6

The length of the lower base of the isosceles trapezoidal is 5+6=11

From the two ends of the upper bottom to the bottom of the perpendicular rock to sell the surplus, the bottom is divided into three sections, the middle section of the long filial piety and the bottom of the same is 4cm

The length of the next two segments: from the right triangle in the corner of the 60 degrees, the beveled side of the length of the thick roll 6 cm, both sections are 3 cm

In the end, it is added up, so the bottom edge length = 3 + 4 + 3 = 10cm

Use the Pythagorean theorem to calculate the length of both sides of the bottom and add the top bottom.

The formula sets the length of the upper bottom a, the height of the h, and the waist length l, then the length of the lower bottom is a+2 (l h).

According to the Pythagorean theorem, there is.

Waist length 2=(bottom - bottom) 2 4 + height 2

Bottom = Top bottom + 2 * (waist length 2 height 2).

At the intersection of the waist and the upper bottom, the auxiliary line is perpendicular to the lower bottom, and the angle between the auxiliary line and the waist is 30 degrees, so the opposite side 12 2 6cm lower bottom upper bottom +6 2 15 + 12 27

So the circumference of the trapezoid is 15+27+2 12 66cm

The two ends of the upper bottom are respectively used as the perpendicular line of the lower bottom, and the lower bottom is divided into three sections, the middle one is equal to the upper bottom, and the other two sections are equal, equal to (8-6) 2=1

Waist length = 2 1 = 2

The bottom is 27cm, analysis: the angle between the bottom and the waist is 60 °, and the bottom is divided into three sections of 6cm, 15cm, and 6cm respectively (the side of the 30 ° angle pair with a right triangle is half of the hypotenuse), so the bottom is 6 + 15 + 6 = 27cm

Solution: Over the top of the bottom of the vertex of the bottom of the perpendicular line, then the high line and the waist angle of 30 degrees, according to the 30 degrees of the right angle side is half of the hypotenuse, easy to get two 6cm, so the bottom = 6 + 6 + 15 = 27cm

Solution: Suppose AB is the top bottom and CD is the bottom bottom.

Through A and B respectively as the bottom of the perpendicular line, the vertical foot is E, F are de=fc=adsin30°=12 1 2=6 cm, then the bottom cd=de+ef+fc=6+15+6=27cm, I hope it can help you.

Happy learning.

o(∩_o~

Go past the apex of the bottom and make a parallel line at the waist.

You can get a parallelogram and an equilateral triangle.

The side length of an equilateral triangle = 17-9 = 8cm

So the waist length of the trapezoidal shape = 8cm