The base of the straight prism is a rhombus. The diagonals of the prism are 10 and 16 cm

| May 13, 2021 | education

The base of the straight prism is a rhombus. The diagonals of the prism are 10 and 16 cm, the side edge is 4 cm. Find the edge of the base.

Through the diagonals of the prism and its height, we determine the lengths of the diagonals of the rhombus at the base of the prism.

Triangles DBB1 and ACC1 are rectangular, then:

AC ^ 2 = AC1 ^ 2 – CC1 ^ 2 = 256 – 16 = 240.

AC = 2 * √60 cm.

BD ^ 2 = DB1 ^ 2 – BB1 ^ 2 = 100 – 16 = 84.

ВD = 2 * √21 cm.

The diagonals of the rhombus ABCD at the point of their intersection are halved and intersect at right angles.

AO = AC / 2 = 2 * √60 / 2 = √60 cm.

BO = BD / 2 = 2 * √21 / 2 = √21 cm.

Triangle AOB is rectangular, then AB ^ 2 = AO ^ 2 + BO ^ 2 = 60 + 21 = 81.

AB = 9 cm.

Answer: The length of the edge of the base is 9 cm.



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