Question

1. a hexagon with a right angle at one vertex, a segment of length 8.7 from the center to that side (perpendicular), and a side length of 10

Explanation:

Step1: Identify the shape and formula

The figure is a regular hexagon (since it has a right angle with the apothem, and regular hexagons can be divided into six equilateral triangles, but here we use the formula for the area of a regular polygon: \( A=\frac{1}{2} \times perimeter \times apothem \)). The apothem (\( a \)) is 8.7, and the side length (\( s \)) is 10. The perimeter (\( P \)) of a hexagon is \( 6s \).

Step2: Calculate the perimeter

Perimeter \( P = 6 \times 10 = 60 \).

Step3: Calculate the area

Using the formula \( A=\frac{1}{2} \times P \times a \), substitute \( P = 60 \) and \( a = 8.7 \):
\( A=\frac{1}{2} \times 60 \times 8.7 \)
First, \( \frac{1}{2} \times 60 = 30 \), then \( 30 \times 8.7 = 261 \).

Answer:

The area of the regular hexagon is \( 261 \) (units², assuming the given units are consistent).