Answer:
45 square units
Explanation:
In the above question, we are given the following values
The ratio of the lengths of the corresponding sides of two regular octagons is 8 to 3.
This means the length of the larger octagon = 8
The length of the smaller octagon = 3
Using scale factor denoted as k and because we are dealing with area of the octagon
k = 3²/8²
The area of the larger octagon is 320 ft².
The area of the smaller octagon s represented as y and is calculated as
k = y/Area of larger octagon
3²/8² = y/320
Cross multiply
8² × y = 3² × 320
y = 3² × 320/8²
y = 45 square units
Area of smaller octagon = 45 square units.