Question

Длина оснований равнобедренной трапеции равны 42 см и 54 см, величина острого угла 30*.Вычисли площадь трапеции.

Answer 1

Ответ:

Пошаговое объяснение:

из вершины прапец. опустить

высоту на нижнее основание.

получится прямоугольный треуголь .

суглом 30°, катет напротив угла в30°

он же высота обозначим х.

гипотенуза=2х ,второй катет 6см

По теореме Пифагора 2х2 -х2=36

х=2 кор.3

площадь=(42+54)/2×2кор.3=

=96кор.из3

Answer 2

Calculating the Area of an Isosceles Trapezoid

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

Area = (1/2) * (a + b) * h

Where: - a and b are the lengths of the parallel sides (the bases) of the trapezoid. - h is the height of the trapezoid, which can be calculated using the Pythagorean theorem and the given angle.

Given: - Length of the bases: 42 cm and 54 cm - Angle: 30 degrees

Calculating the Height of the Trapezoid

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

h = (b - a) / (2 * tan(θ))

Where: - a and b are the lengths of the parallel sides (the bases) of the trapezoid. - θ is the given angle.

Using the given values: - a = 42 cm - b = 54 cm - θ = 30 degrees

We can calculate the height using the formula.

Calculation

h = (54 - 42) / (2 * tan(30°))

h = 12 / (2 * tan(30°))

h = 12 / (2 * 0.5774)

h ≈ 10.3923 cm

Calculating the Area

Now that we have the height, we can calculate the area of the trapezoid using the formula:

Area = (1/2) * (a + b) * h

Substituting the given values: - a = 42 cm - b = 54 cm - h ≈ 10.3923 cm

Area = (1/2) * (42 + 54) * 10.3923

Area ≈ 48 * 10.3923

Area ≈ 498.4616 cm²

So, the area of the trapezoid is approximately 498.4616 cm².