Question

Julie is ordering a stained glass window for the entryway of her house. The window she wants to replace it with is a regular octagon having side lengths of 18 inches and an apothem length of 18.1 inches. What is the area that will be covered by the stained glass?​

A) 15,222.45 sq.inches
B) 18511 sq.iches
C) 18521.98 sq.inches
D) 19000 sq.inches

Answer 1

The area covered by the stained glass window is approximately 18521.98 square inches.

Step-by-step explanation:

To find the area covered by the stained glass window, we need to find the area of the regular octagon. The formula to find the area of a regular octagon is:

Area = (2 + 2√2) × s²

where s is the length of a side.

Given that the side length of the octagon is 18 inches, we can substitute this value into the formula:

Area = (2 + 2√2) × 18²

Simplifying the expression:

Area = (2 + 2√2) × 324

Calculating the area:

Area ≈ 18521.98 square inches