I can help you with that! To find the apothem of a dodecagon (a 12-sided polygon) given the area of 140 square inches, we can use the formula for the area of a polygon:
Area = 1/2 * Perimeter * Apothem
Since we are given the area as 140 square inches, and the dodecagon has 12 sides, we can first find the perimeter of the dodecagon using the formula:
Perimeter = Number of sides * Length of each side
For a dodecagon, the length of each side is not given in the question. However, we can find it by dividing the perimeter into 12 equal sides.
Once we find the perimeter, we can then substitute the known values into the area formula to solve for the apothem. After calculating the apothem, remember to round your answer to the nearest hundredth as requested in the question.
If you have the length of each side or any additional information, please provide it so that we can proceed with the calculations together.
