Question

Основанием пирамиды служит прямоугольник со сторонами 18 см и 24 см, каждое из боковых ребер равно 25 см. Найти площадь сечения, проходящего через диагональ основания и вершину пирамиды.

Answer 1

Площадь бокового сечения 300 см2

Answer 2

Диагналь основания и высоту  находим по теореме Пифагора.Корень из " квадрат стороны основания +квадрат стороны основания". Т.о диагональ=30. а высота 20.Образовано сечение-диагональю основания, вершиной пирамиды и двумя противоположными ребрами. Сечение является треугольником. Площадь треугольника= половина произведения основания на высоту.  Т.е площадь диагонального сечения=0,5*30*20=300

Answer 3

Calculation of the Pyramid's Cross-Section Area

To find the area of the cross-section passing through the diagonal of the base and the vertex of the pyramid, we need to determine the shape of the cross-section.

Given that the base of the pyramid is a rectangle with sides measuring 18 cm and 24 cm, and each of the lateral edges is equal to 25 cm, we can visualize the cross-section as a trapezoid.

Let's calculate the area of the cross-section step by step:

1. Find the length of the diagonal of the base using the Pythagorean theorem: - The diagonal of the base is the hypotenuse of a right triangle with sides measuring 18 cm and 24 cm. - Using the Pythagorean theorem, we can calculate the length of the diagonal (d) as follows: ``` d = sqrt(18^2 + 24^2) ``` Simplifying the equation: ``` d = sqrt(324 + 576) d = sqrt(900) d = 30 cm ``` Therefore, the length of the diagonal of the base is 30 cm.

2. Determine the height of the trapezoid: - The height of the trapezoid is the perpendicular distance between the two parallel sides. - In this case, the height is equal to the length of the lateral edge, which is 25 cm.

3. Calculate the area of the trapezoid using the formula: ``` Area = (a + b) * h / 2 ``` - In this formula, 'a' and 'b' represent the lengths of the parallel sides of the trapezoid, and 'h' represents the height. - In our case, the lengths of the parallel sides are the lengths of the diagonal of the base (30 cm) and the lateral edge (25 cm). - Plugging in the values into the formula: ``` Area = (30 + 25) * 25 / 2 Area = 55 * 25 / 2 Area = 1375 / 2 Area = 687.5 cm^2 ```

Therefore, the area of the cross-section passing through the diagonal of the base and the vertex of the pyramid is 687.5 cm^2.