Question

Периметр равнобедренной трапеции равен 32 см боковая сторона равна 5 см площадь 44 см (квадратных). Найти высоту трапеции.

Answer 1

 назовем трапецию абцд  аб и цд боковые стороны их сумма равна 10 сумма оснований равна 32-10=22 площадь трапеции равна 1/2 полусуммы оснований умножить на высоту  высота равна 4

Answer 2

Perimeter of an Isosceles Trapezoid

To find the height of an isosceles trapezoid, we need to use the given information about the perimeter and the side lengths. Let's break down the problem step by step.

Given information: - Perimeter of the trapezoid = 32 cm - Length of one of the parallel sides (base) = 5 cm - Area of the trapezoid = 44 cm²

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

Area = (base1 + base2) * height / 2

In this case, since the trapezoid is isosceles, the bases are equal in length. Let's denote the length of the bases as 'b' and the height as 'h'.

Area = (b + b) * h / 2

We are given that the area is 44 cm², so we can substitute the values:

44 = (2b) * h / 2

Simplifying the equation, we get:

44 = b * h

Since we know the length of one of the bases is 5 cm, we can substitute 'b' with 5:

44 = 5 * h

Now we can solve for 'h':

h = 44 / 5

Calculating the value, we find:

h ≈ 8.8 cm

Therefore, the height of the trapezoid is approximately 8.8 cm.

Answer

The height of the isosceles trapezoid is approximately 8.8 cm.