If the slant height of a triangular prism is 12 and the lateral edge is 15, then what is the height and the base edge length?

Answer 1

Triangular Prism's do not have a Slant Height, so I assume you mean Triangular Pyramid.

To find the base you would have to use the Pythagorean theorem, which is A²+B²=C². Your "Lateral Edge" is the hypotenuse, so you would set up the equation to be 12²+B²=15². Thus, 144 + B²=225. Therefore, B²= 225-144. Hence, B²= 81. Then you would take the square root of both sides. So B = 9. This "B" is 1/2 of your base. So your base equals 9*2 = 18.

Now that you have your base, since this is a triangular pyramid, all of the base's are the same (since it is a square). One half of the base, height, and slant height form another right triangle. So we will need to use the Pythagorean theorem again. Your slant height in this case, is the hypotenuse. So you will set up the equation 9²+B²=12². Thus, 81+B²=144. Therefore, after subtracting 81 from both sides, B²=63. Thus, B=√63.

BASE = 18

HEIGHT = √63 or 7.94....