In a straight triangular prism, the sides of the bases are 13, 20 and 21, and the height of the prism is 25.
| February 26, 2021 | education
In a straight triangular prism, the sides of the bases are 13, 20 and 21, and the height of the prism is 25. Calculate the area of the section drawn through the lateral rib and the lower height of the base.
By Heron’s theorem, we determine the area of the base of the prism.
The semi-perimeter of triangle ABC is equal to: p = (AB + BC + AC) / 2 = (20 + 13 + 21) / 2 = 27 cm.
Then Sbn = √27 * (27 – 21) * (27 – 17) * (27 – 10) = √27 * 6 * 7 * 14 = √7056 = 126 cm2.
Determine the height of the HВ triangle ABC.
Sosn = AC * ВН / 2.
BH = 2 * Sbn / AC = 2 * 126/21 = 12 cm.
The sectional area is rectangle НН1В1В.
Determine the cross-sectional area.
Ssection = BH * HH1 = 12 * 25 = 300 cm2.
Answer: The cross-sectional area is 300 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.
