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1200.0cm^2
Let's consider the given polygon.
We will first calculate the side length to find the perimeter. Then, we will find the apothem. Finally, since the area of a regular polygon is half the product of the apothem and the perimeter, we will use the obtained values to find the area. Let's do it!
By drawing the 12 radii we can divide the polygon into 12 isosceles triangles. Since the triangles are congruent and a full turn measures 360^(∘), the central angles of the isosceles triangles formed by the radii measure 36012= 30^(∘).
Recall that the apothem bisects the angle and the side of the regular polygon. Therefore, we obtain a right triangle with an acute angle that measures 15^(∘). Let x be the shorter leg of this right triangle.
Substitute values
LHS * 20=RHS* 20
Rearrange equation
Use a calculator
Round to 2 decimal place(s)
Once more, let's consider the right triangle whose longer leg is the apothem of the polygon.
Substitute values
LHS * 20=RHS* 20
Rearrange equation
a= 20cos 15^(∘), p= 124.23
Use a calculator
Round to 1 decimal place(s)