Posted by **Anne** on Monday, December 5, 2011 at 11:54am.

using 100 ft of fence material and building a regular octagon garden, what is the area of the garden?

- math **urgent** -
**Reiny**, Monday, December 5, 2011 at 12:34pm
8 sides, so each side = 12.5 ft

split the octogon into 8 isosceles triangles.

Consider one triangle, the central angle is 360/8 = 45°, so each base angle = 67.5°

tan 67.5 = height/6.25

height = 6.25(tan67.5) = 15.0888...

area of one triangle = (1/2)(12.5)(15.0888..)

= 94.3052..

area of whole thing =8(94.3052..) = 754.4417

check my arithmetic, I had my calculator keep all the digits as I went along

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