Abca1b1c1 straight triangular prism ab = 13 bc = 14 ac = 15 o- the center of the

univerkov | September 17, 2021 | education

Abca1b1c1 straight triangular prism ab = 13 bc = 14 ac = 15 o- the center of the circumscribed circle angle c1oc = 30 find the volume.

By Heron’s theorem, we determine the area of the triangle ABC.

The semi-perimeter of the ABC triangle is: p = (13 + 14 + 15) / 2 = 21 cm.

Then Sас = √21 * (21 – 13) * (21 – 14) * (21 – 15) = √7056 = 84 cm2.

Then R = OC = AB * BC * AC / 4 * Savs = 13 * 14 * 15/4 * 84 = 8.125 cm.

In a right-angled triangle OCC1 CC1 = OC * tg30 = OC / √3.

Then V = Saws * CC1 = 84 * 8.125 / √3 = 682.5 / √3 = 227.5 * √3 cm3.

Answer: The volume of the prism is 227.5 * √3 cm3.

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.