Question

find the volume of the oblique pyramid with a rectangular base. note that the figure is not to scale. enter your answer as a fraction. draw show your work here

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Calculate the area of the rectangular base

The base is a rectangle with length \( l = 5 \) and width \( w=\frac{4}{7} \). The area of a rectangle is \( B=l\times w \), so \( B = 5\times\frac{4}{7}=\frac{20}{7} \).

Step3: Identify the height of the pyramid

The height \( h \) of the pyramid is given as \( \frac{2}{7} \).

Step4: Calculate the volume of the pyramid

Substitute \( B=\frac{20}{7} \) and \( h = \frac{2}{7} \) into the volume formula:
\[
V=\frac{1}{3}\times\frac{20}{7}\times\frac{2}{7}=\frac{1\times20\times2}{3\times7\times7}=\frac{40}{147}
\]

Answer:

\(\frac{40}{147}\)