Question

острый угол равнобедренной трапеции равен 45 градусов а высота проведенная из вершины тупого угла делит основание на отрезки 8 и 34 Найдите площадь трапеции

Answer 1

Тут главное доказать, что треугольники ABF и CDH равны.

Answer 2

I will answer in detail. 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 8 and 34. Find the area of the trapezoid.

To find the area of the trapezoid, we need to know the length of the bases and the height. We are given the height and one of the bases, but we need to find the other base. To do this, we can use the property of an isosceles trapezoid that says that the height, dropped from the vertex of the obtuse angle, divides the larger base into segments that are equal to the half-sum and the half-difference of the bases.

Let AB and CD be the bases of the trapezoid, and let H be the point where the height meets the base AB. Then, we have:

AH = BC + AB / 2

HB = AB - BC / 2

Substituting the given values, we get:

8 = BC + 34 / 2

34 = 34 - BC / 2

Solving for BC, we get:

BC = 13

Now we have the length of both bases, so we can find the area of the trapezoid using the formula:

S = (AB + BC) / 2 * h

S = (34 + 13) / 2 * 8

S = 188

The area of the trapezoid is 188 square units.