# The base of the straight prism is a rhombus. The diagonals of the prism are 8 cm and 5 cm, its height is 2 cm.

December 31, 2020 | education

| **The base of the straight prism is a rhombus. The diagonals of the prism are 8 cm and 5 cm, its height is 2 cm. Calculate the length of the side of the base and the area of the base of the prism.**

From each diagonal of the prism and its height, we can find the corresponding diagonal of the base (rhombus):

d8 = √ (8 ^ 2 + h ^ 2) = √ (64 + 2 * 2) = √68

d5 = √ (5 ^ 2 + h ^ 2) = √ (25 + 2 * 2) = √29

For a rhombus, the ratio is known:

d1 ^ 2 + d2 ^ 2 = 4 * a ^ 2

a = (√d1 ^ 2 + d2 ^ 2) / 4 = √ (68 + 29) / 4 = √97 / 4 = 4.9244 cm – base side length

Sb = (d8 * d5) / 2 = √ (68 * 29) / 4 = √1972 / 4 = √493 = 22.2 cm2 – area of the base of the prism

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