Respuesta :

the radius is √25=5 in this case.
find the area of each triangles first. (the pentagon can be divided into 5 isosceles triangles)
the two equal sides are 5 each, the angle between them is 360/5=72 degree, so the base side is 2*5*sin36, and the height is 5*Cos36
the area of each triangle is (1/2)*2*5*Sin36*5*Cos36
the total area of the 5 triangles is: 5*(1/2)*2*5*Sin36*5*Cos36
use a calculator: A≈59.44

There are 5 isosceles triangles in a regular pentagon and the angle is 36 degrees. Then the area of the regular pentagon is 59.45 square units.

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The area of a regular pentagon inscribed in a circle whose equation is given as

[tex](x-4)^2 + (y+2)^2=25\\\\(x-4)^2 + (y+2)^2=5^2[/tex]

The radius of the circle is 5.

We know that there are 5 isosceles triangles in a regular pentagon. And the angle is 36 degrees.

Then the area of the triangle will be

[tex]\rm Area \ of \ triangle = 2\times \dfrac{1}{2} \times 5 \sin 36^o \times 5\cos 36^o\\\\Area \ of \ triangle = 11.89[/tex]

Then the area of the pentagon will be

Area of pentagon = 5 × 11.89

Area of pentagon = 59.45

More about the polygon link is given below.

https://brainly.com/question/17756657

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