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

Answer: 468 square centimeters

Step-by-step explanation:

The surface area of each of the triangular base is $A=\frac{1}{2}ab$

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 $A=\frac{1}{2}9\cdot12=54\ cm^2$

The third side of triangular base =$H=\sqrt{9^2+12^2}$

$\\\Rightarrow\ H=\sqrt{81+144}\\\Rightarrow\ H=\sqrt{225}\\\Rightarrow\ H=15\ cm$

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

Thus the total lateral area is $10\times9+10\times12+10\times15=10(9+12+15)=10\times36=360\ cm^2$

The total surface area is $=2\times54+360=108+360=468cm^2$

Answer 2

45 I think  is the answer if 9 is the height and 10 is the base then 45 is the answer <span />