Question 604437
I assume that AB is perpendicular to BC
because it's a triangle, then area of triangle:
Area = 1/2 * base * height
Area = 1/2 * 12 * 9 = 6 * 9 = 54 square milimeters


because it's a right triangle, then we can use Phytagoras theorem to find the other side of the triangle:
{{{AB^2 + BC^2 = AC^2}}}
{{{9^2 + 12^2 = AC^2}}}
{{{9^2 + 12^2 = AC^2}}}
{{{81 + 144 = AC^2}}}
{{{225 = AC^2}}}
{{{AC = sqrt(225)}}}
AC = 15 milimeters


Surface Area (SA) of a prism:
SA = 2*base area + base perimeter*prism's height
450 = 2*54 + (9 + 12 + 15)*prism's height
450 = 108 + 36*prism's height
450 - 108 = 36*prism's height
342 = 36 * prism's height
prism's height = 342/36 = 9.5 milimeters


so, the height of the prism is 9.5 millimeters