Question

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?
○ 192 cubic units
○ 200 cubic units
○ 384 cubic units
○ 400 cubic units

Explanation:

Step1: Calculate the area of the rhombus base

The formula for the area of a rhombus is \(A=\frac{1}{2}d_1d_2\), where \(d_1 = 6\) units and \(d_2=8\) units.

$$A=\frac{1}{2}\times6\times8 = 24$$

Step2: Calculate the volume of the prism

The formula for the volume of a prism is \(V = A\times h\), where \(A\) is the area of the base and \(h\) is the height of the prism. Here, \(A = 24\) and \(h = 16\).

$$V=24\times16=384$$

Answer:

384 cubic units