The base of a straight quadrangular prism is a rhombus with a side of 6 and an acute angle

The base of a straight quadrangular prism is a rhombus with a side of 6 and an acute angle of 60 degrees. The smaller diagonal of the prism is 10. Find the side rib.

Since there is a rhombus at the base of the prism, all sides of the base are equal. AB = BC = CD = AD = 6 cm.

Then, in an isosceles triangle ABD, the angle at the vertex B, by condition, is 60, which means that triangle ABD is equilateral and BD = AB = AD = 6 cm.

Since the prisms are straight, the triangle DBB1 is rectangular, and then, by the Pythagorean theorem, we determine the length of the leg BB1.

BB1 ^ 2 = DB1 ^ 2 – BD ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.

BB1 = 8 cm.

AA1 = CC1 = DD1 = BB1 = 8 cm.

Answer: The side edge of the prism is 8 cm.