Question

A parking lot is \(144.3 \mathrm{~m}\) long and 47.66 m wide. (a) What is the perimeter of the lot? (b) What is its area?

Short answer

(a) The perimeter is 383.92 m. (b) The area is 6875.838 m².

Step-by-step solution

Understanding Perimeter

The perimeter of a rectangle is found by adding the lengths of all four sides. Since the opposite sides of a rectangle are equal, the formula is the sum of twice the length and twice the width: \( P = 2 \times (L + W) \).

Calculating Perimeter

Substitute the given length and width into the perimeter formula: \( L = 144.3 \text{ m} \) and \( W = 47.66 \text{ m} \). Thus, the perimeter \( P = 2 \times (144.3 + 47.66) \). Evaluate this to find \( P = 2 \times 191.96 = 383.92 \text{ m} \).

Understanding Area

The area of a rectangle is calculated by multiplying its length by its width. The formula used is \( A = L \times W \).

Calculating Area

Substitute the given length and width into the area formula to find \( A = 144.3 \times 47.66 \). Calculate this to get \( A = 6875.838 \text{ m}^2 \).

Key concepts

Perimeter of a rectangle

The perimeter of a rectangle is like the path you would walk if you strolled all the way around its edges. A rectangle has four sides, with two pairs of opposite sides being equal in length. Here's how you can calculate the perimeter:

• Identify the length (\( L \)) and width (\( W \)) of the rectangle.
• Notice that each of these is repeated twice in the perimeter formula since a rectangle's opposite sides are equal.
• The formula to calculate the perimeter is: \( P = 2 imes (L + W) \).

So, if you know the length is 144.3 m and the width is 47.66 m, then plugging these into the formula gives:\[ P = 2 imes (144.3 + 47.66) = 383.92 ext{ m} \]This calculation tells us that you would walk 383.92 meters if you completed a loop around the parking lot.

Area of a rectangle

The area of a rectangle tells you how much space is inside the shape. Imagine needing to cover the surface of a table or floor; that's the area. Here’s how you determine it:

• Understand that the area is calculated by multiplying the rectangle’s length by its width.
• The formula for area is: \( A = L \times W \).

For our example, with a length of 144.3 m and a width of 47.66 m, the calculation is:\[ A = 144.3 \times 47.66 = 6875.838 ext{ m}^2 \]This means the parking lot covers an area of 6875.838 square meters, enough space to park many cars side by side.

Mathematical calculations

Mathematical calculations involving geometric shapes often follow straightforward formulas, but it's important to understand each component:

• Always check the given measurements, ensuring you understand what each number represents and the units involved.
• When using formulas, carefully substitute the values to avoid errors.
• Simplify the calculations step-by-step, taking care of mathematical operations in sequence.

Accuracy matters, especially when sizing spaces or materials. By thoroughly comprehending each step: calculating twice the added dimensions for perimeter, and multiplying dimensions for area, you ensure precise and meaningful results. These calculations are foundational in geometry and many real-world applications, such as planning construction or understanding spaces.