You have 100 yards of fencing available to create an enclosure for farm animals. as the builder, you can choose one of the design options from below. 4 points option 1: create an enclosure shaped like a regular pentagon. option 2: create an enclosure shaped like a regular hexagon. option 3: create an enclosure shaped like a regular octagon. decide which option will give the animals the most space. show your work and give the area of each enclosure to the nearest tenth of a square yard.

1. area of a pentagon when 1 side is x is
so if perimiter is 100 then one side is 100/5 or 20
area will be ≈688.2 square yards

2. area of a hexagon when 1 side is length x is
so if permiter is 100 then length of one side is 100/6 or about 16.666666666666
the area will be ≈721.7 square yards

3. area of a regular octagon with side lenghts x is
so if 8 sides then side length of each is 100/8 or 12.5
area will be ≈754.4 square yards

octagon wil have most space
you can tell because the more sides it has, the more it gets to a circle and the more area it encloses with a given perimiter

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.