A right prism with rhombus bases is shown. the side length of each rhombus is 5 units. the height of the prism is 16 units. the diagonals of each rhombus measure 6 and 8 units. what is the volume of the prism?

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30-04-2017
Mathematics

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A right prism with rhombus bases is shown. the side length of each rhombus is 5 units. the height of the prism is 16 units. the diagonals of each rhombus measure 6 and 8 units. what is the volume of the prism?

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BlueSky06 BlueSky06 · Answer 1 · 2017-05-13T08:06:52+02:00

To determine the volume of the rhombus, we use the equation,
V = Bh
where B is the area of the base and h is the height.
For rhombus, the area is calculated through the equation,
B = D₁D₂/2
Substituting,
B = (6)(8) / 2 = 24 units squared

Volume calculation:
V = (24)(16) = 384 units cubed

astha8579 astha8579 · Answer 2 · 2022-02-21T13:31:36+01:00

Area of rhombus is half of its diagonals' lengths' product. The volume of the specified prism is 384 cubic units.

How to find the area of rhombus from its diagonals' lengths?

Suppose that a rhombus is there with diagonals p and q units, then its area is

Area = pq/2 sq. units.

How to find volume of a right prism?

Volume of a right prism = Bh cubic units, where B is the Base's area and h is its height.

For the given case, we have the base's area as:

B = 6× 8/2 = 24 sq units.

Since height is given to be 16 units, thus,

Volume of considered prism = 24 × 16 = 384 cubic units.

Thus, The volume of the specified prism is 384 cubic units.

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