HELP ME GUYS PLEASE , I AM ILLITERATE the cross section of a prism is a triangle having base angles each 60 degree . if the height of prism is 6√3 cm and volume 162cm^3 , find the side of the cross - section.

6

Step-by-step explanation:

volume of prism = area of cross section * height

area of cross section =162/6√3 =27/√3

since the base angles are each 60 degrees, the triangle is an equilateral triangle. for equilateral triangles, area =(√3 * side^2)/4

hence,

27/√3 = (√3 * side^2)/4

side^2 = (27/√3) / (√3/4) = 108/3 = 36

side = ±√36 = 6 or -6 (rej as side >0)