Question

Боковая сторона равнобокой трапеции с углом при основании 30 градусов равна 10 см , а диогональ 25см.Найти площадь трапеции.

Answer 1

Высота трапеции=10/2=5 см (как катет против угла 30 градусов)
полусумма оснований=v(25^2-5^2)=v(625-25)=v600=10v6
площадь=10v6*5=50v6 см.кв.

Answer 2

Calculation of the Trapezoid's Area

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

Area = (a + b) * h / 2

Where: - a and b are the lengths of the parallel sides (bases) of the trapezoid. - h is the height of the trapezoid, which is the perpendicular distance between the bases.

In this case, we are given the following information: - One of the bases of the trapezoid has a length of 10 cm. - The diagonal of the trapezoid has a length of 25 cm. - The angle at the base of the trapezoid is 30 degrees.

Let's calculate the length of the other base and the height of the trapezoid using the given information.

Calculation of the Length of the Other Base

To find the length of the other base, we can use the diagonal and the angle at the base of the trapezoid. We can divide the trapezoid into two right triangles and use trigonometry to find the length of the other base.

Let's denote the length of the other base as x.

Using the sine function, we can write the following equation:

sin(30 degrees) = x / 25

Simplifying the equation, we have:

x = 25 * sin(30 degrees)

Using a calculator, we can find that sin(30 degrees) = 0.5.

Substituting the value of sin(30 degrees) into the equation, we have:

x = 25 * 0.5 = 12.5 cm

Therefore, the length of the other base is 12.5 cm.

Calculation of the Height of the Trapezoid

To find the height of the trapezoid, we can use the Pythagorean theorem. We can consider the diagonal as the hypotenuse of a right triangle, with the height as one of the legs and the difference between the lengths of the bases as the other leg.

Let's denote the height of the trapezoid as h.

Using the Pythagorean theorem, we can write the following equation:

h^2 = 25^2 - (12.5 - 10)^2

Simplifying the equation, we have:

h^2 = 625 - 2.5^2

h^2 = 625 - 6.25

h^2 = 618.75

Taking the square root of both sides, we have:

h = sqrt(618.75) ≈ 24.85 cm

Therefore, the height of the trapezoid is approximately 24.85 cm.

Calculation of the Area of the Trapezoid

Now that we have the lengths of the bases and the height of the trapezoid, we can calculate its area using the formula mentioned earlier.

Substituting the values into the formula, we have:

Area = (10 + 12.5) * 24.85 / 2

Calculating the expression, we find:

Area ≈ 11.25 * 24.85 / 2 ≈ 139.78 cm^2

Therefore, the area of the trapezoid is approximately 139.78 square centimeters.

Please note that the calculations are rounded for simplicity.