Question

A package 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

Answer 1

the answer is 436 i just took the test

Answer 2

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:


`\displaystyle{√(9^2+12^2)= √(81+144)= √(225)=15` (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)


Answer: 436 (square cm)