Question

Острый угол равнобедренной трапеции равен 45, а высота, проведенная из вершины тупого угла, делит основание на отрезки 14 см.и 34 см. Найдите площадь трапеции.(желательно с рисунком)

Answer 1

У меня получилось476

Answer 2

1 . S = a + b / 2 * h
2 . b = 34 + 14 = 48
3 . a = 34 - ( 14 + 14 ) = 6
4 . h = 14 ( т. к. АН = ВН , где ВН - высота проведённая из тупого угла 
5 . S = 6 + 48 / 2 * 14 = 378 .

Answer 3

Given Information:

We are given that the acute angle of an isosceles trapezoid is 45 degrees, and the height drawn from the vertex of the obtuse angle divides the base into segments of 14 cm and 34 cm.

Solution:

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

Area = (1/2) * (sum of the lengths of the parallel sides) * height

In this case, the lengths of the parallel sides are the segments of the base, which are 14 cm and 34 cm. The height is the length of the line drawn from the vertex of the obtuse angle to the base.

Let's calculate the area step by step:

1. First, let's find the length of the line drawn from the vertex of the obtuse angle to the base. Since the trapezoid is isosceles, the height is also the perpendicular bisector of the base. This means that the height divides the base into two equal segments. Therefore, the length of the height is equal to half the sum of the lengths of the base segments.

Length of the height = (14 cm + 34 cm) / 2 = 48 cm / 2 = 24 cm

2. Now, we can substitute the values into the formula to find the area:

Area = (1/2) * (14 cm + 34 cm) * 24 cm = (1/2) * 48 cm * 24 cm = 24 cm * 24 cm = 576 cm^2

Therefore, the area of the trapezoid is 576 cm^2.

Diagram:

Here is a diagram to help visualize the given information and the solution:

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