A regular pentagon may be divided into 5 congruent triangles.
If the side of the pentagon is 6 feet, each base of the triangles will be 6 feet.
If the distance from the center to a vertex is 6 feet, all the sides of the triangles will 6 feet.
So there are 5 congruent, equilateral triangles each with side equal to 6 feet.
The area one of those triangles is calculateb by:
base * height / 2
height ^2 = (side length) ^2 - (side length /2)^2 = 6^2 - 3^2 = 36 - 9 = 27
=> height = √(27) ≈ 5.2 feet
And, using area = base * height / 2 ,
area of a triangle = 6 feet * 5.2 feet / 2 = 15.6 feet^2
And the area of the entire pentagon equals 5 triangles ≈ 5 * 15.6 feet^2 = 78 feet^2
Answer: 78 feet^2
