Let's denote the side length of each square as x. Since the area of a square is equal to the side length squared, we can write:
Area of each square = x^2 = 8
Taking the square root of both sides, we get:
x = ā8 = 2ā2
Since the intersection of the three equal squares is a regular triangle, we can calculate its area using the formula:
Area of a regular triangle = (s^2ā3)/4
where s is the length of each side of the triangle. In this case, s is the side length of each square, so s = 2ā2.
Area of the triangle = (2ā2^2ā3)/4 = 4ā3
Given that the area of the entire shape is 16, and the area of the triangle is 1, we can calculate the area of the three black pentagons by subtracting the sum of the areas of the squares and the triangle from the total area.
Area of the three black pentagons = 16 - (3 * 8 + 1) = 16 - (24 + 1) = 16 - 25 = -9
The area of the black pentagon is -9. However, since area cannot be negative, there might be an error in the given information or calculations. Please double-check your question or provide additional information.