Question

Find the area of a regular pentagon with the apothem of 24.3 cm and a side length of 35.3

Answer 1

Answer: $A=2144\ cm^2$

Step-by-step explanation:

For this exercise you need  to use the following formula for calculate the area of regular polygon:

$A=\frac{s^2n}{4tan(\frac{180}{n})}$

Where is "s" the length of any side, "n" is the number of sides.

Int this case you know that it is regular pentagon, which means that it has five sides. Then you can identify that the values of "n" and "s":

$s=35.3cm\\n=5$

 Therefore, substituitng values into the formula, you get that the area f the pentagon is:

$A=\frac{(35.3cm)^2(5)}{4tan(\frac{180}{5})}\\\\A=2144\ cm^2$