A straight prism is based on a rhombus with a side of 5 cm and a diagonal of 8 cm.

| May 15, 2021 | education

A straight prism is based on a rhombus with a side of 5 cm and a diagonal of 8 cm. Calculate the volume of the prism if the diagonal of the side face = 13 cm.

Since there is a rhombus at the base of the prism, its diagonals are perpendicular and are divided in half at the point of intersection.

Then ОА = СО = АС / 2 = 8/2 = 4 cm, and triangle AOB is rectangular.

By the Pythagorean theorem, we determine the length of the leg OB.

OB ^ 2 = AB ^ 2 – AO ^ 2 = 25 – 16 = 9.

OB = 3 cm.

Then ВD = 2 * ОВ = 2 * 3 = 6 cm.

In a right-angled triangle DCD1, the leg CD = AB = 5 cm, since all sides of a rhombus are equal, then: DD1 ^ 2 = CD1 ^ 2 – CD ^ 2 = 169 – 25 = 144.

DD1 = 12 cm.

Determine the area of the base of the prism.

Sbn = АС * ВD / 2 = 8 * 6/2 = 24 cm2.

Then V = Sbn * DD1 = 24 * 12 = 288 cm3.

Answer: The volume of the prism is 288 cm3.



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