In A Regular N- Gon The Sides Are 4.8 Cm In Length The Apothem Is 7.4 Cm And The Area Is 117.6 Cm How Many Sides Are In The Polygon
in a regular n- gon the sides are 4.8 cm in length the apothem is 7.4 cm and the area is 117.6 cm how many sides are in the polygon
Answer:
10 sides
Step-by-step explanation:
in a regular n- gon the sides are 4.8 cm in length the apothem is 7.4 cm and the area is 177.6 cm² how many sides are in the polygon (i guess the given is 177.6)
Given: A = 177.6 cm²
s (length of side) = 4.8 cm
a (apothem) = 7.4 cm
Required: number of sides
Solution:
use the formula for finding the area of regular polygon with apothem:
A = ( a × p) / 2 where p is the perimeter of the regular polygon
p = sn where n is the number of sides
A = ( a × sn) / 2
n = (2A) / (a × s)
n = (2 × 177.6) / (7.4 × 4.8)
n = 10 sides
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