The base of the straight prism is a right-angled triangle with legs of 6 and 8 dm

| April 13, 2021 | education

The base of the straight prism is a right-angled triangle with legs of 6 and 8 dm, the diagonal of the larger side face is 10√2 dm. find the total surface area of the prism

Since the triangle ABC is rectangular, then by the Pythagorean theorem, we determine the length of the hypotenuse of the AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 64 + 36 = 100.

AC = 10 cm.

Since the prism is straight, the lateral edge of AA1 is perpendicular to the base, then the triangle AA1C is rectangular, in which we determine the length of the leg AA1.

AA1 ^ 2 = A1C ^ 2 – AC ^ 2 = 200 – 100 = 100.

AA1 = 10 cm.

Let us determine the area of ​​the lateral surface of the prism.

Sside = Ravs * AA1 = (6 + 8 + 10) * 10 = 240 cm2.

Determine the area of ​​the base of the prism.

Sosn = AB * BC / 2 = 8 * 6/2 = 24 cm.

Then Sпов = 2 * Sсн + S side = 2 * 24 + 240 = 288 cm2.

Answer: The total surface area of ​​the prism is 288 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.