Question

Высота проведенная из вершина тупого угла равнобедренной Трапеции делит большее основание на части длиной 6 см и 12 см.Найти среднюю линию трапецию.

Answer 1

Ответ: 12 см

Пошаговое объяснение:

1) Опускаем высоту из тупого угла

2) Видно, что если сделать то же действие с другим углом, то средний отрезок большего основания равен 6 и при этом образовывает прямоугольник с верхним основанием. Тогда верхнее основание тоже равно 6

3) По формуле на фото находим среднюю линию

Answer 2

Task: Find the length of the median of an isosceles trapezoid

To find the length of the median of an isosceles trapezoid, we need to know the lengths of the two bases and the height drawn from the vertex of the obtuse angle. In this case, the trapezoid has one base with a length of 6 cm and the other base with a length of 12 cm. We need to find the length of the median.

Let's solve this step by step:

1. First, let's label the trapezoid. We'll call the shorter base AB, the longer base CD, and the height from the vertex of the obtuse angle E.


2. Since the trapezoid is isosceles, the legs (the sides that are not the bases) are congruent. Let's call the length of the legs x.

3. We can use the Pythagorean theorem to find the length of the legs. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle ADE, where AE is the height and AD is the hypotenuse. The length of AE is given as 6 cm.

Applying the Pythagorean theorem, we have:

AD^2 = AE^2 + DE^2

AD^2 = 6^2 + x^2

AD^2 = 36 + x^2

4. Now, let's consider the trapezoid ABCD. We know that the median of a trapezoid is the line segment connecting the midpoints of the legs. Let's call the midpoint of AB as M and the midpoint of CD as N.


5. Since M and N are midpoints, we can say that AM = MB and CN = ND. Therefore, the length of MN is equal to the average of the lengths of AB and CD.

MN = (AB + CD) / 2

MN = (6 + 12) / 2

MN = 18 / 2

MN = 9 cm

6. Now, let's find the length of AD, which is the hypotenuse of the right triangle ADE. We can use the Pythagorean theorem equation we derived earlier:

AD^2 = 36 + x^2

Since we know that MN is the median, it is also equal to AD. Therefore, we can substitute MN for AD:

MN^2 = 36 + x^2

9^2 = 36 + x^2

81 = 36 + x^2

x^2 = 81 - 36

x^2 = 45

x = √45

x ≈ 6.71 cm

7. Therefore, the length of the median of the isosceles trapezoid is approximately 6.71 cm.

Please note that the calculations provided are based on the information given in the question. If there are any additional details or constraints, the answer may vary.