Question

12. The diagram shows a regular pentagon of side 10 cm with a star inside. Calculate the area of the star

Please answer without any confusion ​

Answer 1

Answer:

which lesson is this when you tell them we give answer

Answer 2

Answer:

81.3

Step-by-step explanation:

The middle part of the star forms a pentagon and we that

each side of a regular pentagon has an angle of 108

therefor, XOP = AOE = 108

And AOF = 108/2 = 54

so, OAF = 180-54-90 = 36

Let FO be m

By using the properties of similarity

5/sin(53) = m/sin(36)

There for

5/sin(54)*sin(36) = 3.63271264

so, area of the triangle = 1/2*b*h

1/2*10*3.63271264 = 18.1635632

there are 5 triangle so,

18.1635632*5 = 90.817816

Total area of pentagon = 1/4*$\sqrt{5(5+s\sqrt{5}) }$ *side^2

Area = 172.0477401

Area of the star = area of the pentagon - area of the triangle

172.0477401 - 90.817816 = 81.22992406

Area of the star = 81.2 (rounded)