Question

Четыре стола в форме трапеции нужно поставили вкруговую для проведения групповой работы. боковые стороны устанавливают вплотную друг другу. Углы при основании трапеции равны 45 градусов, основния отличаются в 3 раза, а расстояние между основаниями равно 600 мм. Найди площадь получеенного стала.

Answer 1

Ответ:

2,88 м²

Пошаговое объяснение:

((х+2*0,6)*4)/(4х)=3

х=0,6

0,6+2*0,6=1,8

1,8²-0,6²=2,88

Answer 2

Problem Analysis

We have four trapezoidal tables arranged in a circular formation for group work. The side edges of the tables are placed closely together, and the angles at the base of the trapezoid are 45 degrees. The bases of the trapezoids differ in length by a factor of 3, and the distance between the bases is 600 mm. We need to find the area of the resulting table.

Solution

To find the area of the resulting table, we can break it down into two parts: the area of the trapezoids and the area of the space between them.

# Area of the Trapezoids

The area of a trapezoid can be calculated using 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

In our case, the bases of the trapezoids differ in length by a factor of 3. Let's assume the shorter base is x mm. Then the longer base would be 3x mm. The height of the trapezoid can be calculated using the formula:

h = (3x - x) / 2 = 2x

Therefore, the area of each trapezoid can be calculated as:

Area of each trapezoid = (x + 3x) * 2x / 2 = 4x^2

# Area of the Space Between the Trapezoids

The space between the trapezoids forms a circle with a radius equal to half the distance between the bases of the trapezoids. In our case, the distance between the bases is 600 mm, so the radius of the circle would be 600 / 2 = 300 mm.

The area of a circle can be calculated using the formula:

Area = π * r^2

where: - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the circle

Therefore, the area of the space between the trapezoids can be calculated as:

Area of the space between the trapezoids = π * 300^2

# Total Area of the Resulting Table

To find the total area of the resulting table, we need to sum the areas of the trapezoids and the area of the space between them.

Total Area = 4 * (Area of each trapezoid) + (Area of the space between the trapezoids)

Now let's calculate the values and find the total area.

Calculations: - Let x be the length of the shorter base of the trapezoid. - The longer base would be 3x. - The height of the trapezoid is 2x. - The area of each trapezoid is 4x^2. - The radius of the space between the trapezoids is 300 mm. - The area of the space between the trapezoids is π * 300^2.

Total Area = 4 * (4x^2) + (π * 300^2)

Now we can calculate the total area.