If an office space is 72 feet wide and has a perimeter of 410 feet, what is its area?

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Calculating the Area of the Office Space

To find the area of the rectangular office space, we first need to understand the relationship between the width, length, and perimeter of a rectangle.

We know the following:

  • Width (W) = 72 feet
  • Perimeter (P) = 410 feet

Understanding the Perimeter Formula

The formula for the perimeter of a rectangle is:

P = 2(W + L)

Where:

W = Width

L = Length

Finding the Length

We can rearrange the formula to solve for the length (L):

410 = 2(72 + L)

Let’s simplify this step by step:

  1. First, divide both sides by 2:
  2. 205 = 72 + L
  3. Now, subtract 72 from both sides:
  4. L = 205 – 72
  5. L = 133 feet

Calculating the Area

The area (A) of a rectangle is calculated using the formula:

A = W * L

Now, substitute the values we have:

A = 72 feet * 133 feet

A = 9576 square feet

Conclusion

Thus, the area of the rectangular office space is 9576 square feet.

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