The base side of a regular triangular prism is 10, the height of the prize is 153√3. Calculate

The base side of a regular triangular prism is 10, the height of the prize is 153√3. Calculate the volume and surface area of the prism.

Since the prism is correct, there is a regular triangle with a side of 10 cm at its base.

Then Sbn = BC * √3 / 4 = 10 * √3 / 4 = 5 * √3 / 2 cm2.

Then Vpr = Ssc * АА1 = (5 * √3 / 2) * 153 * √3 = 1147.5 cm3.

Since ABC is a regular triangle, the areas of the side faces are equal, then S side = 3 * SАСС1А1 =

3 * 10 * 153 * √3 = 4590 * √3 cm2.

Then Sprize = 2 * Sb + S side = 2 * 5 * √3 / 2 + 4590 * √3 = 4595 * √3 cm2.

Answer: The area of the prism is 4595 * √3 cm2, the volume of the prism is 1147.5 cm3.