Find the length of the diagonal of the prism.
left 12 cm
bottom 3 cm
right 4cm
To find the length of the diagonal of the prism, we need to use the Pythagorean theorem.
First, we need to find the height of the prism. Since the bottom face has dimensions of 3cm by 4cm, and the left face has a length of 12cm, we can create a right triangle with the height as the hypotenuse.
Let's call the height of the prism "h."
Using the Pythagorean theorem, we have:
h^2 = 12^2 - 3^2
h^2 = 144 - 9
h^2 = 135
h ≈ √135
h ≈ 11.61 cm
Now, we can find the length of the diagonal. This is the hypotenuse of the right triangle with sides of 11.61cm, 3cm, and 4cm.
Using the Pythagorean theorem again, we have:
Diagonal^2 = 11.61^2 + 3^2 + 4^2
Diagonal^2 = 134.92 + 9 + 16
Diagonal^2 ≈ 159.92
Diagonal ≈ √159.92
Diagonal ≈ 12.65 cm
Therefore, the length of the diagonal of the prism is approximately 12.65 cm.