Question

в равнобедренной трапеции тупой угол равен 135 градусов высота проведённая из вершины этого угла делит основание трапеции на отрезки 8,9 см и 17,9 см найдите площадь трапеции(25баллов)

Answer 1

Ответ: 4,76 см^2

Объяснение:

Answer 2

Given Information:

We are given that in an isosceles trapezoid, the obtuse angle is 135 degrees. The height drawn from the vertex of this angle divides the base of the trapezoid into segments of 8.9 cm and 17.9 cm. We need to find the area of the trapezoid.

Solution:

To find the area of the trapezoid, we can use the formula:

Area = (sum of the lengths of the parallel sides) * (height) / 2

In this case, the parallel sides are the two bases of the trapezoid, and the height is the length of the line segment drawn from the vertex of the obtuse angle to the base of the trapezoid.

Let's calculate the area step by step:

1. First, let's find the length of the line segment drawn from the vertex of the obtuse angle to the base of the trapezoid. This length is the height of the trapezoid.

According to the given information, the height divides the base into segments of 8.9 cm and 17.9 cm. Since the height is drawn from the vertex of the obtuse angle, it forms a right triangle with the two segments of the base.

Using the Pythagorean theorem, we can find the length of the height:

height^2 = (8.9 cm)^2 + (17.9 cm)^2

Solving this equation, we find:

height ≈ 19.8 cm

2. Now that we have the height, let's find the sum of the lengths of the parallel sides (the bases of the trapezoid).

Since the trapezoid is isosceles, the lengths of the two parallel sides are equal. Let's denote this length as 'x'.

According to the given information, the height divides the base into segments of 8.9 cm and 17.9 cm. Therefore, we can write the equation:

8.9 cm + x + x + 17.9 cm = 2x + 26.8 cm

Solving this equation, we find:

2x ≈ 26.8 cm - 8.9 cm - 17.9 cm

2x ≈ 26.8 cm - 26.8 cm

2x ≈ 0 cm

Since the sum of the lengths of the parallel sides is 2x, and 2x is equal to 0 cm, we can conclude that the sum of the lengths of the parallel sides is 0 cm. This means that the trapezoid degenerates into a line segment.

Therefore, the area of the trapezoid is 0.

Answer:

The area of the trapezoid is 0 square centimeters.