The diagonal of a regular four-sided prism is 13 cm and the diagonal of the side of the face
| June 2, 2021 | education
The diagonal of a regular four-sided prism is 13 cm and the diagonal of the side of the face is 12 cm. Find the area of the base of the prism.
Since the prism is correct, the lateral faces are perpendicular to the base of the prism, then the AB1 diagonal is also perpendicular to AD, since the diagonal belongs to the lateral face, and AD belongs to the base of the prism.
Consider a right-angled triangle AB1D, whose leg AB1 = 12 cm, and the gitenuse DB = 1 cm, then by the Pythagorean theorem: AD ^ 2 = DB1 ^ 2 – AB ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25 …
AD = 5 cm.
The side of the base is 5 cm, then Sbn = 5 * 5 = 25 cm2.
Answer: The base area of the prism is 25 cm3.
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