Answers

2016-04-17T16:54:45+08:00

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
No. of diagonals = n(n-3)/2
35 = n(n-3)/2
70 = n² - 3n
0 = n² - 3n - 70
0 = (n - 10)(n + 7)

Since n is positive, n is 10. Thus, the polygon has 10 sides

Length of apothem (distance from center to midpoint of a side)
10 =  \frac{side}{2tan( \frac{180}{n} )}
10 =  \frac{s}{2tan(180/10)}
20 =  \frac{s}{tan(18)}
20 tan(18) = s
s = 20 (0.3249)
s = 6.498

Area of a regular n-sided polygon
= n * side * apothem/2
= 10 * 6.498 * 10/2
= 649.8/2
= 324.9 cm²

0