The regular pentagon can divide into 5 congruent isosceles triangles
The equal sides of each triangle have length r and vertex angle of measure 72 degrees
Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon
Since the radius is 7mm, then
r = 7
[tex]A=5\times\frac{1}{2}\times r\times r\times sin72[/tex]
Substitute r by 7
[tex]\begin{gathered} A=5\times\frac{1}{2}\times7\times7\times sin72 \\ \\ A=116.5044232\text{ mm}^2 \end{gathered}[/tex]
Round it to the nearest whole number
A = 117 mm^2
The area of the pentagon is 117 mm^2
