Which formula gives the perimeter of a parallelogram with base a and side b?

Which formula gives the perimeter of a parallelogram with base a and side b?

• A. p = 2(a + b)
• B. p = a + b
• C. p = 2ab
• D. p = a^2 + b^2

Answer: (A)

In a parallelogram, opposite sides are equal, so you have two sides of length a and two sides of length b. Adding all four sides gives a + a + b + b = 2a + 2b, which simplifies to 2(a + b). This is the perimeter because it adds every side around the shape. The other expressions don’t fit: a + b would only count one of each side, 2ab is the area of a rectangle with sides a and b, and a^2 + b^2 relates to the diagonal length in a right triangle, not the perimeter.

In a parallelogram, opposite sides are equal, so you have two sides of length a and two sides of length b. Adding all four sides gives a + a + b + b = 2a + 2b, which simplifies to 2(a + b). This is the perimeter because it adds every side around the shape. The other expressions don’t fit: a + b would only count one of each side, 2ab is the area of a rectangle with sides a and b, and a^2 + b^2 relates to the diagonal length in a right triangle, not the perimeter.