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Perimeter: 61.2m
Area: 282.7m^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 8 radii we can divide the polygon into 8 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 3608= 45^(∘).
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 22.5^(∘). Let x be the shorter leg of this right triangle.
Substitute values
LHS * 10=RHS* 10
Rearrange equation
Use a calculator
Round to 1 decimal place(s)
Once more, let's consider the right triangle whose longer leg is the apothem of the polygon.
Substitute values
LHS * 10=RHS* 10
Rearrange equation
a= 10cos 22.5^(∘), p= 61.2
Use a calculator
Round to 1 decimal place(s)