Apackage is in the shape of a triangular prism. the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. the distance between the bases is 10 centimeters. what is the surface area of the triangular prism? square centimeters

Note that the surface area of the prism is the sum of the surface areas of the 3 lateral faces and the 2 identical bases. 

The bases are each right triangles with side lengths 9, and 12 cm. By the Pythagorean theorem we find that the length of the hypotenuse is:

(cm).

(we can also notice that the triangle is the special case 3:4:5 multiplied by a factor of 3, so 9:12:15).

The surface area of each of the triangular bases is (1/2)*9*12=54 (square cm)

The lateral areas are each a rectangle of dimensions 10 by 9, 10 by 12, and 10 by 15.

Thus the total lateral area is 10*(9+12+15)=10*36=360 (square cm).

The total surface area is 2*54+360=108+360=436 (square cm)

436 (square cm)