Question

ПОМОГИТЕ ПОЖАЛУЙСТА СРОЧНО основание равнобокой трапеции ABCD равна 11 см и 23 см а высота 8 см Найдите а)диагональ трапеции ACB)радиус окружности описывающие около трапеции​

Answer 1

Ответ:

Диагональ равна $\sqrt{353}$ см,

$R=\frac{115\sqrt{353} }{184}$

Объяснение:

Решение в приложении. Ответы некрасивые

Answer 2

Problem Analysis

We are given a trapezoid ABCD with the following measurements: - Base AB = 11 cm - Base CD = 23 cm - Height h = 8 cm

We need to find: a) The length of diagonal AC b) The radius of the circle circumscribing the trapezoid

Solution

a) To find the length of diagonal AC, we can use the Pythagorean theorem. In a trapezoid, the diagonals are perpendicular to each other, so we can consider triangle ABC.

Using the Pythagorean theorem, we have: AC^2 = AB^2 + BC^2

To find BC, we can subtract the length of the shorter base from the longer base and divide by 2: BC = (CD - AB) / 2

Substituting the given values, we have: BC = (23 - 11) / 2 = 6 cm

Now we can calculate AC: AC^2 = AB^2 + BC^2 = 11^2 + 6^2 = 121 + 36 = 157 AC = √157 ≈ 12.53 cm

Therefore, the length of diagonal AC is approximately 12.53 cm.

b) To find the radius of the circle circumscribing the trapezoid, we can use the formula: r = (AC * h) / (2 * area)

The area of a trapezoid can be calculated using the formula: area = ((AB + CD) * h) / 2

Substituting the given values, we have: area = ((11 + 23) * 8) / 2 = 34 * 8 / 2 = 136 cm^2

Now we can calculate the radius: r = (AC * h) / (2 * area) = (12.53 * 8) / (2 * 136) ≈ 0.58 cm

Therefore, the radius of the circle circumscribing the trapezoid is approximately 0.58 cm.

Summary

- The length of diagonal AC in the trapezoid ABCD is approximately 12.53 cm. - The radius of the circle circumscribing the trapezoid is approximately 0.58 cm.