Given a coordinate plane with parallelogram PQRS, where point P is at (-2, 5), point Q is at (2, 1), point R is at (1, -2), and point S is at (-3, 2), and with SR = 4‚Äöao2 and QR = ‚Äöao10, what is the perimeter of parallelogram PQRS?

Mathematics Questions

Given a coordinate plane with parallelogram PQRS, where point P is at (-2, 5), point Q is at (2, 1), point R is at (1, -2), and point S is at (-3, 2), and with SR = 4‚Äöao2 and QR = ‚Äöao10, what is the perimeter of parallelogram PQRS?

Short Answer

The perimeter of parallelogram PQRS is calculated by first identifying the lengths of its adjacent sides, SR (4‚Äöao2) and RQ (‚Äöao10). Applying the perimeter formula, the result is 2(‚Äöao10 + 4‚Äöao2), which simplifies to 2‚Äöao10 + 8‚Äöao2.

Step-by-Step Solution

Step 1: Understand Parallelogram Properties

Before calculating the perimeter, it’s essential to review some key properties of a parallelogram. These properties include:

Each pair of opposite sides are parallel.
Each pair of opposite sides are equal in length.
The perimeter is calculated as twice the sum of the lengths of two adjacent sides.

Step 2: Identify Side Lengths

Next, identify the lengths of the adjacent sides of parallelogram PQRS. In this case:

The length of side SR is 4‚Äöao2.
The length of side RQ is ‚Äöao10.

These lengths will be used in the perimeter calculation.

Step 3: Calculate the Perimeter

Now, we can compute the perimeter of parallelogram PQRS using the formula:

Perimeter = 2(RQ + SR).

Substituting the values, we have:

Perimeter = 2(‚Äöao10 + 4‚Äöao2).
This simplifies to 2‚Äöao10 + 8‚Äöao2.

Thus, the perimeter of parallelogram PQRS is 2‚Äöao10 + 8‚Äöao2.

Given a coordinate plane with parallelogram PQRS, where point P …