Problem 334 - Prealgebra

Question

In the following exercises, solve. Home decor Shawnte bought a rug for the hall of her apartment. The rug is 3 feet wide by 18 feet long. What is the area of the rug?

Step-by-Step Solution

Answer

54 square feet

Step 1: Understand the Problem

Identify the dimensions of the rug. The width is 3 feet, and the length is 18 feet. The goal is to find the area of the rug.

Step 2: Recall the Formula for Area

The area of a rectangle is given by the formula: \[\text{Area} = \text{Length} \times \text{Width}\]

Step 3: Substitute the Given Dimensions

Substitute the given dimensions into the area formula: \[\text{Area} = 18 \text{ feet} \times 3 \text{ feet}\]

Step 4: Calculate the Area

Perform the multiplication to find the area: \[18 \times 3 = 54\]Therefore, the area of the rug is 54 square feet.

Key Concepts

problem-solving

Solving math problems involves a systematic approach. It starts with understanding the problem itself. In our example with Shawnte's rug, we first identified the dimensions of the rug. Breaking down the problem step-by-step can help make it manageable.

This method includes:

• Identifying what is given: Here, the width is 3 feet and the length is 18 feet.
• Determining what needs to be found: The area of the rug.
• Using appropriate formulas or methods to solve the problem, like the area formula for rectangles.

This structured approach ensures that we do not miss any important details. Don't rush through the steps—understanding each part is key to accurate problem-solving.

multiplication

Multiplication is one of the basic arithmetic operations that you regularly use in everyday life, including in geometry problems. It involves adding a number to itself a certain number of times.

For our rug problem, we needed to multiply the length by the width. Mathematically, this means:
\[ 18 \times 3 \]
Breaking it down simply:

• Multiplying means taking 18, three times: \[18 + 18 + 18\]
• The result is 54.

If multiplication is tricky, try breaking down the numbers further or using multiplication tables as practice. Understanding how to multiply effectively will make solving area problems much easier.

geometry

Geometry is the branch of mathematics that studies the sizes, shapes, and properties of figures and spaces. One simple figure in geometry is the rectangle, which has opposite sides that are equal and four right angles.

In our problem, the rug is a rectangle. Understanding the properties of rectangles helps in calculating area and other measurements. Important properties include:

• Opposite sides are equal length.
• All angles are right angles (90 degrees).
• The area is found by multiplying the length by the width.

By knowing these properties, we can easily apply the correct formula to find the rug's area.

area calculation

Calculating the area of a rectangle involves using a simple formula. Area measures the amount of space inside a shape. The formula for the area of a rectangle is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
In the rug example, we substituted 18 feet (length) and 3 feet (width) into the formula:
\[ \text{Area} = 18 \text{ feet} \times 3 \text{ feet} = 54 \text{ square feet} \]
This tells us the rug covers 54 square feet of space. Remembering that area is always in square units is essential. So, if you ever need to find out how much space something covers, use the right formula and units to get an accurate result.