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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