Question

В равнобедренной трапеции с основанием 10 см и 24 см , боковая сторона равна 25 см . Найдите высоту.

Answer 1

Допустим, АВСД - трапеция, АВ и СД - ее основания, чертим две высоты ВК и СН, получился прямоугольник ВКНС, следовательно ВС=КН=10(см), отсюда АК=ДН=0.5 (АД -КН)=0.5(14)=7(см)
АВК - прямоугольный треугольник, отсюда ВК = √АВ²-АК² = √625-49=√576=24(см)
Ответ: 24 см.

Answer 2

Finding the Height of an Isosceles Trapezoid

To find the height of an isosceles trapezoid with a base of 10 cm, a top of 24 cm, and a side of 25 cm, we can use the Pythagorean theorem to calculate the height.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the height of the trapezoid as h, and the two bases as a and b. In this case, a = 10 cm, b = 24 cm, and the side is 25 cm.

Calculating the Height

Using the Pythagorean theorem, we can calculate the height (h) of the trapezoid:

h^2 = 25^2 - ((24-10)/2)^2 h^2 = 625 - 7^2 h^2 = 625 - 49 h^2 = 576 h = √576 h = 24 cm

The height of the isosceles trapezoid is 24 cm.

This calculation is based on the Pythagorean theorem and the dimensions provided for the trapezoid