Question

find the volume of the oblique rectangular prism below. round your answer to the nearest tenth if necessary.
answer attempt 1 out of 2
units³ submit answer

Explanation:

Step1: Recall Volume Formula for Prism

The volume \( V \) of a rectangular prism (oblique or right) is given by the formula \( V = \text{Base Area} \times \text{Height} \). The base is a rectangle with length \( l = 6 \) and width \( w = 4 \), so the base area \( A = l \times w \).
\( A = 6 \times 4 = 24 \)

Step2: Identify the Height

For an oblique prism, the height is the perpendicular distance between the two bases. Here, the perpendicular height is \( 12 \) (not the slant length \( 17 \)).

Step3: Calculate Volume

Using the volume formula \( V = A \times h \), substitute \( A = 24 \) and \( h = 12 \).
\( V = 24 \times 12 = 288 \)

Answer:

\( 288 \)