Question

Основы прямоугольной трапеции равняются 9 см и 4 см , , а её большая диагональ =15 см Найти периметр трапеции . Помогите , пожалуйста!

Answer 1

Ответ:

12+13+4+9=38см......

Answer 2

Calculation of the Perimeter of a Trapezoid

To find the perimeter of a trapezoid, we need to know the lengths of its bases and the lengths of its two non-parallel sides. In this case, we are given the lengths of the bases and the length of the larger diagonal.

Let's denote the lengths of the bases as a and b, and the length of the larger diagonal as d. In this case, a = 9 cm, b = 4 cm, and d = 15 cm.

To calculate the perimeter of the trapezoid, we can use the formula:

Perimeter = a + b + c + d

where c is the length of the smaller diagonal.

To find the length of the smaller diagonal, we can use the formula for the diagonals of a trapezoid:

c = √(d^2 - ((a - b)^2 / 4))

Let's substitute the given values into the formula:

c = √(15^2 - ((9 - 4)^2 / 4))

Simplifying the equation:

c = √(225 - (5^2 / 4))

c = √(225 - 25/4)

c = √(225 - 6.25)

c = √(218.75)

c ≈ 14.8 cm

Now, we can substitute the values of a, b, c, and d into the perimeter formula:

Perimeter = 9 cm + 4 cm + 14.8 cm + 15 cm

Perimeter ≈ 42.8 cm

Therefore, the perimeter of the trapezoid is approximately 42.8 cm.

Please note that the calculations are approximate due to rounding.