Question

Найдите площадь равнобедренной трапеции, если ее меньшее основание равно 18 см высота 9 см и острый угол равен 45 градусов! решить с объяснениями подробными!

Answer 1

Площадь трапеции вычисляется по формуле: S=(h*(a+b))/2, где a и и - основания, а h - высота трапеции.
Найдем основание AD. Оно равно сумме AH, BC и  ED. AH=BH=9 см, так как ABH это равнобедренный прямоугольный треугольник.
AD=AH+HE+ED=9+18+9=36 см
Площадь трапеции:
S=(9*(18+36))/2=9*27=243  кв.см
Ответ: 243 см^2

Answer 2

Finding the Area of an Isosceles Trapezoid

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

Area = (a + b) * h / 2

where: - a and b are the lengths of the bases of the trapezoid - h is the height of the trapezoid

In this case, the smaller base of the trapezoid is given as 18 cm and the height is given as 9 cm. We need to find the length of the larger base.

To find the length of the larger base, we can use the fact that the trapezoid is isosceles and that one of the angles is 45 degrees.

Let's denote the length of the larger base as x. Using trigonometry, we can set up the following equation:

x = 2 * (18 * tan(45°/2))

Now, we can substitute the values into the area formula:

Area = (18 + x) * 9 / 2

Let's calculate the area step by step.

1. Calculate the length of the larger base (x): - Using the formula x = 2 * (18 * tan(45°/2)): - x = 2 * (18 * tan(22.5°)) - x ≈ 2 * (18 * 0.4142) - x ≈ 14.85 cm

2. Calculate the area of the trapezoid using the formula Area = (18 + x) * 9 / 2: - Area = (18 + 14.85) * 9 / 2 - Area ≈ 32.33 cm²

Therefore, the area of the given isosceles trapezoid is approximately 32.33 cm².

Please note that the above calculations are based on the given information and assumptions about the trapezoid. If there are any additional details or constraints, the calculations may vary.