# If each side of parallelogram P has length 1, what is the area of P

If each side of parallelogram P has length 1, what is the area of P?

1. One angle of P measures 45 degrees.
2. The altitude of P is √2/2.

To determine the area of the parallelogram, you need to know the base (which is given as 1), and the height of the parallelogram. So, you need to know the height of the parallelogram only.

Statement 1: One angle of P measures 45 degrees.

Hence, you can draw the parallelogram as:

△ABC is a right-angled triangle. The sum of all angles of the triangles is 180°.

90° + 45° + ∠ACB = 180°

∠ACB = 45°

Hence, △ABC is a 45-45-90 triangle.

The side ratio in a 45-45-90 is 1 : 1 : √2. Thus, BC = h = √2.

You can find out the area of the triangles. Hence, statement 1 is sufficient to find the answer to the question.

Statement 2: The altitude of P is √2/2.

As altitude is given, you can find out the area of the triangles. Hence, statement 2 is sufficient to find the answer to the question.

The correct option is D.