Final answer:
The mathematical shape that possesses both a perimeter and a diameter is a Circle (A). In this context, the perimeter refers to the circumference and is calculated as 2πr, while the diameter is simply 2r.
Step-by-step explanation:
The shape in mathematics that has the concept of both perimeter and diameter is A) Circle. The perimeter of a circle is commonly known as its circumference, and it can be calculated using the formula 2πr (where π is approximately 3.14159 and r is the radius). The diameter of a circle is twice the radius, so it can be expressed as 2r. If we consider a circle inscribed within a square, the diameter of the circle will be equal to the side length of the square, noted as a = 2r. Consequently, the circumference (perimeter) of the circle will indeed be somewhat around 6r or 3a, fitting into the intuitive reasoning that the perimeter is between two times and four times the side length of the inscribing square (2a and 4a respectively).