At the base of a straight prism lies a rhombus with an acute angle of 60 degrees and a side of 6

| September 1, 2021 | education

At the base of a straight prism lies a rhombus with an acute angle of 60 degrees and a side of 6 centimeters. Find the smaller diagonal of the prism. If its side edge is 8 centimeters.

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

In triangle ABD AB = AD, then triangle ABD is isosceles. Since in an isosceles triangle ABD one of the angles is 60, then triangle ABD is equilateral, then BD = 6 cm.

In a right-angled triangle BB1D, according to the Pythagorean theorem, we determine the length of the hypotenuse DB1.

DB1 ^ 2 = BB1 ^ 2 + BD ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100.

DB1 = 10 cm.

BD is the smaller diagonal of the rhombus ABCD, since it lies against a smaller angle, then the diagonal DB1 is the smaller diagonal of the prism.

Answer: The smaller diagonal of the prism is 10 cm.



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