## Task 2 - 290812

The base of a right prism is an equilateral triangle with a given side length $a$. The sum of all edge lengths of this prism is $15 a$.

Calculate the surface area of the lateral surface of this prism!
A straight prism is a solid whose base and top faces are parallel congruent polygons and whose side faces are rectangles.

In the mentioned prism, the sum of the lengths of the top and base edges is 6a, so $15 a-6 a=9 a$ remains for the sum of the three side edge lengths; each side edge therefore has a length of $3 a$.

The area $A_{M}$ of the lateral surface is thus $A_{M}=9 a^{2}$.