The center of the pentagon in arlington, virginia, is a courtyard in the shape of a regular pentagon. the pentagon could be inscribed in a circle with a radius of 300 feet. find the area of the courtyard. round to the nearest tenth.

Step-by-step explanation:

If the pentagon is inscribed inside a circle with 300 feet of radius, that means the radius of the pentagon is also 300 feet.

A pentagon can be divided in five equal isosceles triangle, where the vertex angle of each on is

Now, each isosceles triangle can be divided in to equal right triangles with an angle equal to

Additionally, the hypothenuse of each right triangle is the radius, so .

We can find the leg that represent the height of the triangle by using trigonometric reasons

Where the height.

The base would be

Then, the are of one triangle would be

This means the area of one triangle is 13252.5 square feet.

However, a pentagon is formed by 5 triangles. So, the are would be