# 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 One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.