Question

this oblique triangular prism has a volume of $63\\ \mathrm{cm}^3$.

what is the area of the base of the prism?

$\square\\ \mathrm{cm}^2$

Explanation:

Step1: Recall the volume formula for a prism

The volume \( V \) of a prism is given by the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height (the perpendicular distance between the two bases).

Step2: Identify the given values

We know the volume \( V = 63 \, \text{cm}^3 \) and the height \( h = 6 \, \text{cm} \) (the perpendicular height, as indicated by the dashed line with the right angle).

Step3: Solve for the base area \( B \)

Rearrange the volume formula to solve for \( B \): \( B = \frac{V}{h} \).

Substitute the given values: \( B = \frac{63}{6} \).

Step4: Calculate the result

\( \frac{63}{6} = 10.5 \).

Answer:

\( 10.5 \)