At the base of a straight prism there is a right-angled triangle, the legs of which are 6 cm and 8 cm.

| March 17, 2021 | education

At the base of a straight prism there is a right-angled triangle, the legs of which are 6 cm and 8 cm. Lateral edge of the prism 12. Find the total surface area of the prism and its volume.

Since there is a right-angled triangle at the base of the prism, its area will be equal to:

Savs = AB * BC / 2 = 8 * 6/2 = 24 cm2.

Let’s define the volume of the prism.

Vpr = Sbn * АА1 = 24 * 12 = 288 cm3.

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

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

AC = 10 cm.

Since the prism is straight, the side faces of the prism are rectangles, then: Sside = P * AA1, where P is the perimeter of the base of the prism.

P = AB + BC + AC = 8 + 6 + 10 = 24 cm.

Side = 24 * 12 = 288 cm2.

Then Spol = 2 * Sb + S side = 2 * 24 + 288 = 336 cm2.

Answer: The volume of the prism is 288 cm3, the total surface area is 336 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.