Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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 platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.