Question

СРОЧНООООО !!! РЕШИТЬ ПОЛЬНОСТЬ И С ОБЬЯСНЕНИЯМИ!!!!! !!! ПОЖАЙЛУСТА !!! Нехай АВСD А1 В1 С1 D1 - прямокутний паралелепіпед, ав=4см, аd= 3см, aa1= 6см .Знайти площу перерізу даного прямокутного паралелепіпеда площиною , що проходить через пряму ВD і точку N -середину АА1 .

Answer 1

BD =√(AD^2 +AB^2) =5

NB =√(AN^2 +AB^2) =5

ND =√(AN^2 +AD^2) =3√2

Формула Герона для р/б треугольника (a - боковые стороны, b - основание)

S =b/2 √(a^2 -(b/2)^2)

S =3/2 √2 √(25 -9/2) =1,5√41 (см^2)  ~9,6

Answer 2

To find the area of the cross-section of the rectangular parallelepiped, we need to determine the shape of the cross-section and then calculate its area. In this case, the cross-section passes through the line BD and the midpoint N of AA1.

Determining the shape of the cross-section:

To determine the shape of the cross-section, we can consider the plane that contains the line BD and the midpoint N of AA1. Since the line BD is parallel to the base of the parallelepiped, the cross-section will be a rectangle.

Calculating the dimensions of the cross-section:

To calculate the dimensions of the cross-section, we need to find the lengths of the sides of the rectangle. Let's denote the length of the cross-section as l and the width as w.

Since the cross-section passes through the midpoint N of AA1, we can consider the triangle AAN. The line segment AN is the median of the triangle AAN, which means it divides the base AA1 into two equal parts. Therefore, AN = NA1 = 6 cm.

Since the cross-section passes through the line BD, we can consider the triangle BDN. The line segment BD is the median of the triangle BDN, which means it divides the base BD1 into two equal parts. Therefore, BD = BD1 = 4 cm.

Now, let's consider the triangle BAD. We can use the Pythagorean theorem to find the length of the line segment AD. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In triangle BAD, the sides AB and BD are known. AB = 3 cm and BD = 4 cm. Let's calculate AD using the Pythagorean theorem:

AD^2 = AB^2 + BD^2 AD^2 = 3^2 + 4^2 AD^2 = 9 + 16 AD^2 = 25 AD = 5 cm

Therefore, AD = 5 cm.

Now, we have the dimensions of the cross-section: l = AD = 5 cm and w = BD = 4 cm.

Calculating the area of the cross-section:

To calculate the area of the cross-section, we can use the formula for the area of a rectangle: A = length * width.

Substituting the values, we have: A = l * w A = 5 cm * 4 cm A = 20 cm^2

Therefore, the area of the cross-section of the given rectangular parallelepiped is 20 cm^2.

Please note that the calculations provided above are based on the given dimensions and assumptions.