what is the area of the pentagon with a radius of 7mm?

Given:
Radius of the pentagon = 7 mm
Let'd find the area of the pentagon.
A pentagon is a polygon with 5 sides.
To find the area of a pentagon, let's first find the length of each side of the pentagon.
We have a sketch below:
Apply the trigonometric ratio formula for tangent:
[tex]tan\theta=\frac{opposite\text{ }}{adjacent}[/tex]Where:
θ = 36 degrees
opposite side = x
Adjacent side = 7 mm
Let's solve for x:
[tex]\begin{gathered} tan36=\frac{x}{7} \\ \\ x=7tan36 \\ \\ x=5.09\text{ mm} \end{gathered}[/tex]Therefore, the length of each side will be:
s = x + x = 5.09 + 5.09 = 10.18 mm
To find the area, apply the formula:
[tex]A=\frac{n*s*a}{2}[/tex]Where:
A is the area
n is the number of sides = 5
s is the length of each side = 10.18 mm
a is the radius = 7 mm
Thus, we have:
[tex]\begin{gathered} A=\frac{5*10.18*7}{2} \\ \\ A=\frac{356.006}{2} \\ \\ A=178\text{ mm}^2 \end{gathered}[/tex]Therefore, the area of the pentagon is mm².
• ANSWER:
mm².