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.

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