Sandra built an enclosure for her rabbit in the shape of a regular octagon. The perimeter of the enclosure is 24 feet and the area is 43.26 square feet. What value represents the approximate length of the apothem?

4.7 ft
3.6 ft
3.9 ft
1.9 ft

9514 1404 393

  3.6 ft

Explanation:

Apparently, you're supposed to use the formula ...

  A = (1/2)Pa

where A is the area, P is the perimeter, and 'a' is the apothem.

  a = 2A/P = 2(43.26)/24 ≈ 3.605

The apothem is about 3.6 feet.

Comment on the problem

For whatever reason, problems involving the use of the apothem are often inconsistently written. This one is no exception. The formula for the area in terms of side length is ...

  A = 2(1 +√2)s²

The apothem is ...

  a = s/(2·tan(22.5°))

For the given perimeter, A ≈ 43.46 square feet, and 'a' ≈ 3.621 ft.

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