Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

A regular pentagon is inscribed in a circle whose radius measures 9 inches. Find the area of the pentagon.

Sagot :

CamilleEaton210
Since the Pentagon can be divided into 5 equal triangles, and each of the angle opposite the sides of the pentagon is 360/5 = 72 degree. 

Also, since each of the 5 triangles from the divided pentagon is an isoceles triangle (same 2 sides = radius), the 2 base angles are equal. Base angle = (180 - 72)/2 = 54. 

Using Sine Law to calculate side of the Pentagon: 
Side/sin(72) = radius /sin(54) = 9/sin(54) 
Side = 10.58 

Therefore each triangle has an area of: 
= 0.5(side)(radius)sin(54) = 0.5(10.58)(9)sin(54) 
= 38.52 

Total area of Pentagon = 5 x 38.52 = 192.60

Answer:

Step-by-step explanation:

View image cristygardea3
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.