Problem 335 - Prealgebra

Question

In the following exercises, solve. Room size The meeting room in a senior center is rectangular, with length 42 feet and width 34 feet. What is the area of the meeting room?

Step-by-Step Solution

Answer

The area of the meeting room is 1428 square feet.

Step 1: Understand the problem

First, identify that the problem is asking for the area of a rectangular meeting room. The given dimensions are the length (42 feet) and the width (34 feet).

Step 2: Recall the formula for the area of a rectangle

The area of a rectangle can be found using the formula: \[ \text{Area} = \text{Length} \times \text{Width} \]

Step 3: Plug in the given values

Substitute the length and width into the formula: \[ \text{Area} = 42 \text{ feet} \times 34 \text{ feet} \]

Step 4: Calculate the area

Multiply the length by the width: \[ 42 \times 34 = 1428 \] So, the area of the meeting room is 1428 square feet.

Key Concepts

Rectangular Dimensions

Rectangular shapes are all around us. From rooms and buildings to screens and books, understanding their dimensions is crucial. A rectangle has four sides, with opposite sides being equal in length. Its two longer sides are called the length, and the two shorter sides are called the width. In our example of the meeting room, the dimensions are:

• Length: 42 feet
• Width: 34 feet

When you know the length and the width, you're set to find out more about the rectangle's properties, like its area.

Area Calculation

Calculating the area of a rectangle is about finding how much space it covers. The formula to find the area of a rectangle is: \[ \text{Area} = \text{Length} \times \text{Width} \] Here’s how we use this formula with the dimensions of the meeting room: 42 feet (length) and 34 feet (width). By substituting the values into the formula, we get: \[ \text{Area} = 42 \text{ ft} \times 34 \text{ ft} = 1428 \text{ sq ft} \] That means the meeting room covers an area of 1428 square feet. It’s like figuring out how many square tiles you need to completely cover the floor without any gaps!

Geometry Fundamentals

Geometry helps us understand and describe the physical world. One of the basics of geometry is knowing how to work with different shapes, such as rectangles. Key terms:

• Length: The longer side of a rectangle.
• Width: The shorter side of a rectangle.
• Area: The total space within the rectangle's boundaries, measured in square units.

For rectangles, it's important to remember that by multiplying the length by the width, you can find the area. This idea is not just limited to floors—think about walls, screens, or any flat rectangular surfaces you encounter in everyday life. Mastering these fundamental concepts provides a strong foundation for exploring more complex geometric shapes and calculations.