For Exercises 35 to 38, make drawings as needed.
In regular octagon ABCDEFGH, the length of each side is In terms of s, find an expression for
a) HE, the length of diagonal .
b) the area of .
a. The length of HE.
In a regular octagon ABCDEFGH, each side of the octagon is s.
We have to find the length of the diagonal HE in the octagon.
Consider the diagonals HE, BG and CF.
Here, GFYX is a rectangle. So XY = GF=s.
To find HX, Consider the triangle HGX
Side HG=s, here the angles are because it is an isosceles right triangle.
By the theorem ,
A 45-45-90 degree triangle is a triangle with angles of and the sides are in the ratio 1:1:
By the above theorem,
b. The area of the triangle HED.
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