Question

1. (a regular pentagon with side length 8 and apothem 5.5, likely to find the area or perimeter etc.)

Explanation:

Step1: Identify the shape and formula

The figure is a regular pentagon? Wait, no, actually, the formula for the area of a regular polygon is \( A=\frac{1}{2} \times perimeter\times apothem \). Wait, the apothem is 5.5, and one side is 8. A pentagon has 5 sides, so perimeter \( P = 5\times8=40 \).

Step2: Calculate the area

Using the formula \( A=\frac{1}{2}\times P\times a \), where \( P \) is perimeter and \( a \) is apothem.
Substitute \( P = 40 \) and \( a = 5.5 \) into the formula:
\( A=\frac{1}{2}\times40\times5.5 \)
First, \( \frac{1}{2}\times40 = 20 \)
Then, \( 20\times5.5=110 \)

Answer:

The area of the pentagon is 110.