In a straight parallelepiped ABCDA’B’C’D ‘, the sides of the base are AB = 3cm, AD = 8cm, and the angle between
| March 8, 2021 | education
In a straight parallelepiped ABCDA’B’C’D ‘, the sides of the base are AB = 3cm, AD = 8cm, and the angle between them is 60 °. The diagonal cross-sectional area of BB’D’D is 70cm2. Determine the side surface of the box.
In triangle ABD, we apply the cosine theorem and determine the length of the diagonal BD of the parallelepiped.
BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * Cos60 = 9 + 64 – 2 * 3 * 8 * 1/2 = 73 – 24 = 49.
ВD = 7 cm.
The area of the diagonal section of a parallelepiped is a rectangle.
Then Ssech = BD * BB1.
BB1 = Ssection / BD = 70/7 = 10 cm.
Determine the area of the lateral surface of the parallelepiped.
Sside = Rosn * BB1 = 2 * (3 + 8) * 10 = 220 cm2.
Answer: The lateral surface area is 220 cm2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
