In a rectangular parallelepiped, the sides of the base are 6 and 8 cm. The diagonal of the parallelepiped

| June 15, 2021 | education

In a rectangular parallelepiped, the sides of the base are 6 and 8 cm. The diagonal of the parallelepiped makes an angle of 45 degrees with the plane of the base. Find the side edge and side surface of the parallelepiped.

Since the parallelepiped is straight, all its faces and bases are rectangles.

Let us construct a diagonal AC, then the angle ACA1 is the angle between the diagonal and the plane of the base, the angle ACA1 = 45.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + AD ^ 2 = 36 + 64 = 10.

AC = 10 cm.

In a right-angled triangle ACA1, one of the acute angles is 45, then the legs of this triangle are equal.

AA1 = AC = 10 cm.

The area of ​​the side surface of the parallelepiped will be:

Sside = Ravsd * AA1 = 2 * (AB + AD) * AA1 = 2 * (6 + 8) * 10 = 280 cm2.

Answer: The lateral rib is 10 cm, the lateral surface area is 280 cm2.



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