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Yakvenalex [24]
3 years ago
10

I’m struggling with this question , geometry

Mathematics
1 answer:
just olya [345]3 years ago
7 0

The exterior angles of a regular <em>n</em>-gon add up to 360º; here <em>n</em> = 9, so each exterior angle has measure (360/9)º = 40º.

Corresponding interior angles are supplementary to exterior angles (they add to 180º), so each interior angle has measure (180 - 40)º = 140º.

Bisect this angle by connecting any given vertex to the center of the nonagon. These connections split up the nonagon into 9 congruent isosceles triangles, each of which have base angles of 70º.

Split each triangle in half to make a total of 18 70º-20º-90º triangles with height <em>h</em> and base <em>b</em>. Then

sin70º = <em>h</em>/7  ==>  <em>h</em> = 6.578

sin20º = <em>b</em>/7  ==>  <em>b</em> = 2.394

and each right triangle has an area of approximately 1/2 <em>b</em> <em>h</em> = 7.874.

Multiply this by 18 to get the area of the nonagon: 141.7.

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