Answer:
area = 18.81 m²
Explanation:
solving for the 7 sided polygon first:
divide into 7 equal isosceles triangles, each having sides of 10 m and a peak angle of 360°/7 = 51.43°. Drop a line from the peak & perpendicular to the base makes a right triangle with a 25.71° peak angle and a 10 m hypotenuse.
sin 25.71° = x/10, x = 4.34, the base of the full triangle will be 2 x 4.34 = 8.68 m
cos 25.71° = x/10, x = 9.01, the rise of the triangle is 9.01 m
The area of each triangle will be 1/2(8.68)(9.01) = 39.10 m²
39.10 x 7 triangles = 273.72 m²
area of 7 sided polygon = 273.72 m²
Next solve for the inner circle:
The rise of the triangle (9.01) is the radius of the inner circle.
area of inner circle = πr² = 3.14(9.01²) = 254.91 m²
273.72 - 254.91 = 18.81 m²