The pentagon below has an area of 8.3 square centimeters and a side of 2.2. What is the approximate length of the apothem? A.0.4 cm B.0.8 cm C.1.5 cm D.1.9 cm

Accepted Solution

Answer:C. 1.5 cmStep-by-step explanation:A pentagon is a polygon with 5 sides.  The formula for the area of a regular polygon is[tex]A=\frac{1}{2}ap[/tex]where a is the apothem and p is the perimeter.  The perimeter is found by multiplying the number of sides of the figure by the length of 1 of those sides:5(2.2) = 11Now we have everything we need to solve for the length of the apothem.  [tex]8.3=\frac{1}{2}a(11)[/tex]Begin by multiplying both sides by 2 to get rid of the fraction, so16.6 = 11a  Divide both sides by 11 to geta = 1.5090909 orC. 1.5 cm