   Chapter 11.1, Problem 40E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For Exercises 35 to 38, make drawings as needed.In regular octagon ABCDEFGH, the length of each side is s . In terms of s, find an expression fora) HE, the length of diagonal H E - .b) the area of △ H E D .

To determine

To find:

a. The length of HE.

Explanation

Given:

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.

Therefore, HE=HX+XY+YE

Here, GFYX is a rectangle. So XY = GF=s.

To find HX, Consider the triangle HGX

Side HG=s, here the angles are 45°-45°-90° because it is an isosceles right triangle.

By the theorem 45°-45°-90°,

A 45-45-90 degree triangle is a triangle with angles of 45°,45°,90° and the sides are in the ratio 1:1:2

By the above theorem, H

To determine

To find:

b. The area of the triangle HED.

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