In a regular triangular prism, the side of the base is 8cm, and the diagonal of the side face is 10cm.

In a regular triangular prism, the side of the base is 8cm, and the diagonal of the side face is 10cm. Find the area of the lateral surface of the prism.

In a regular triangular prism, the diagonal of the side face, the side of the base and the height of the prism make up a right-angled triangle, in which the hypotenuse is the diagonal of the side face, and the legs are the height and side of the base of the prism.

We know that the side of the base is 8 cm and the diagonal is 10 cm.

Let the height of the prism be x and using the Pythagorean theorem we can calculate it:

10² = 8² + x²,

х² = 10² – 8²,

x² = 36,

x = 6.

Now we can find the lateral surface area of this prism:

S = 3 * 6 * 8 = 144 cm².