At the base is a right-angled triangle, the angle C is 90 degrees, the dihedral angles at the base are equal

At the base is a right-angled triangle, the angle C is 90 degrees, the dihedral angles at the base are equal, the legs of a right-angled triangle of the wound are 6 and 8 cm.The height of the pyramid is 1. find the total surface area

If the dihedral angles at the base -а are equal, then the base of the height is the center of the inscribed circle, and the base of the pyramid is the orthogonal projection of the lateral surface of the pyramid. It remains to find out the area of the base and the cosine of the dihedral angle at the base, which is equal to the ratio of the radius of the inscribed circle of the base – r – to the apothem of the pyramid – h.

Base hypotenuse – with:

c = √ (6 ^ 2 + 8 ^ 2) = 10 (cm).

r = 2S / P = 6 * 8 / (6 + 8 + 10) = 2 (cm).

h = √ (2 ^ 2 + 1 ^ 2) = √5 (cm).

cos a = 2 / √5.

S side pov = S main / cos a = 24 / (2 / √5) = 12 √5 (cm ^ 2).

S full turn = (24 + 12 √5) cm ^ 2.