The base of the straight prism is a right-angled triangle with legs 6 and 8 dm, the diagonal of the larger

The base of the straight prism is a right-angled triangle with legs 6 and 8 dm, the diagonal of the larger side face is 10√2 dm. find the total surface area of the prism.

Since the triangle ABC is rectangular, then by the Pythagorean theorem, we determine the length of the hypotenuse of the AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 64 + 36 = 100.

AC = 10 dm.

Determine the area of the base of the prism.

Sosn = AB * BC / 2 = 8 * 6/2 = 24 dm.

Triangle AA1C is rectangular, then let us determine the length of the leg AA1.

AA1 ^ 2 = A1C ^ 2 – AC ^ 2 = 200 – 100 = 100.

AA1 = 10 dm.

Let us determine the area of the lateral surface of the prism.

Sside = Ravs * AA1 = (6 + 8 + 10) * 10 = 240 dm2.

Then Sпов = 2 * Sсн + Sbok = 2 * 24 + 240 = 288 dm2.

Answer: 288 dm2.