The diagonal of a regular four-angle prism is 3.5 cm, and the diagonal of the side face is 2.5 cm.

| August 4, 2021 | education

The diagonal of a regular four-angle prism is 3.5 cm, and the diagonal of the side face is 2.5 cm. Find the volume of the prism.

Consider a right-angled triangle AC1B, and by the Pythagorean theorem we determine the length of the leg AB.

AB ^ 2 = BC1 ^ 2 – AC1 ^ 2 = 3.5 ^ 2 – 2.5 ^ 2 = 12.25 – 6.25 = 6.

AB = √6 cm.

Since the pyramid is correct, AB = BC = SD = AC = √6 cm.

Consider a right-angled triangle ACC1 and, by the Pythagorean theorem, determine the length of the leg CC1, which is the height of the prism.

CC1 ^ 2 = AC1 ^ 2 – AC ^ 2 = 2.5 ^ 2 – (√6) ^ 2 = 6.25 – 6 = 0.25.

CC1 = √0.25 = 0.5 cm.

Determine the area of the base of the prism.

Sb = √6 * √6 = 6 cm2.

Let’s define the volume of the prism.

V = Sbn * CC1 = 6 * 0.5 = 3 cm3.

Answer: The volume of the prism is 3 cm3.



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