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

45 I think is the answer if 9 is the height and 10 is the base then 45 is the answer

Answer 2

Answer: 468 square centimeters

Explanation:

The surface area of each of the triangular base is
`A=(1)/(2)ab`

where a and b are the perpendicular legs of triangle (the triangular base must be right triangle)

⇒The surface area of each of the triangular base
`A=(1)/(2)9\cdot12=54\ cm^2`

The third side of triangular base =
`H=√(9^2+12^2)`

`\\\Rightarrow\ H=√(81+144)\\\Rightarrow\ H=√(225)\\\Rightarrow\ H=15\ cm`

Then the lateral areas of each rectangle of dimensions 10 × 9, 10 × 12, and 10 × 15.

Thus the total lateral area is
`10*9+10*12+10*15=10(9+12+15)=10*36=360\ cm^2`

The total surface area is
`=2*54+360=108+360=468cm^2`