Question

this prism has a lateral area of 432 square centimeters. the base is a regular octagon. find the length of one side of the base. 9 cm

Explanation:

Step1: Recall the formula for the lateral area of a prism

The lateral area \( L \) of a prism is given by the formula \( L = Ph \), where \( P \) is the perimeter of the base and \( h \) is the height (or length) of the prism.

Step2: Identify the given values

We know that the lateral area \( L = 432 \) square centimeters and the height \( h = 9 \) centimeters. The base is a regular octagon, so let the length of one side of the octagon be \( s \). The perimeter \( P \) of a regular octagon is \( 8s \) (since a regular octagon has 8 equal sides).

Step3: Substitute the values into the formula and solve for \( s \)

Substitute \( L = 432 \), \( h = 9 \), and \( P = 8s \) into the formula \( L = Ph \):
\[
432 = 8s \times 9
\]
First, simplify the right - hand side: \( 8s\times9=72s \)
So the equation becomes:
\[
432 = 72s
\]
To solve for \( s \), divide both sides of the equation by 72:
\[
s=\frac{432}{72}
\]
\[
s = 6
\]

Answer:

6