The area of the regular pentagon is 929.2486 or 929.2.
What is regular pentagon?
A pentagon is geometrical shapes with" five sides and five angles". The 'pen' represents five and 'gon' represents 'angle' .
According to the question,
The regular pentagon has 'O' as its center and radius of regular pentagon is 17.
Formula for Area of regular apothem:1/2×(perimeter of polygon)× apothem
Find the length of the apothem
tan θ = [tex]\frac{opposite}{adajacent}[/tex]
To find θ
The sum of the angles divided by number of sides and to find sum of the angles is (n-2)180.
(12-2)180 = (10)(180).55
= 1800.
To find entire interior angle 1800 divided by 8 we get 225.For the triangle at the bottom of the diagram, the angle is half tha is 225 divided by 5 is 15°.
tan 15° = [tex]\frac{x}{17}[/tex]
(0.2679) 17 = x
x = 4.5543
Perimeter of the polygon = (4.5543)(17)
= 77.4231
Formula for Area of regular apothem:1/2×(perimeter of polygon)× apothem
=77.4231 × 12
=929.2476
Hence, The area of the regular pentagon is 929.2486 or 929.2.
Learn more about regular pentagon here
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