Question

The length of a rectangle is 24 inches, and the width of the rectangle is 18 inches. What is the area?

Short answer

The area of the rectangle is 432 square inches.

Step-by-step solution

Identify Key Information

The problem states that the length of the rectangle is 24 inches and the width is 18 inches. We need to use these measurements to find the area of the rectangle.

Understand the Formula for Area

The area of a rectangle is calculated by multiplying the length by the width. The formula is: \[ \text{Area} = \text{Length} \times \text{Width} \]

Plug in the Values

Substitute the given values into the formula for area: \[ \text{Area} = 24 \text{ inches} \times 18 \text{ inches} \]

Perform the Calculation

Multiply the length and width to find the area: \[ 24 \times 18 = 432 \text{ square inches} \]

Write the Answer

The area of the rectangle is 432 square inches.

Key concepts

Understanding the Area of a Rectangle

Calculating the area of a rectangle is like understanding how much surface the shape covers. The area is the space inside the rectangle's borders. To find this, we use a simple mathematical trick. You multiply the rectangle's length by its width. In essence, counting how many small squares can fit within the rectangle. Each square has sides that are one unit long.

In the given problem, the length and width are special because they play a key role in determining the area. Imagine if each inch was a tiny square. You'd stack these squares column by column. This helps visualize why multiplying gives the area. It's not just a formula – it's a neat way of seeing the size of your object. Think of it as counting all the squares inside a rectangle quickly.

Exploring Rectangular Dimensions

Dimensions tell you how big an object is. In rectangles, these dimensions are usually the length and width. Length is how long the rectangle stretches, while width is how wide it is. These dimensions are important because they determine the shape and size of your rectangle.

In our example, the rectangle has a length of 24 inches and a width of 18 inches. This means that it is much longer than it is wide, forming an elongated shape. Knowing these dimensions allows you to understand more about the rectangle than just its area. You could even calculate the perimeter, or if you're creating something, understand how much material you'd need.

• Length: the longer side of the rectangle (24 inches)
• Width: the shorter side of the rectangle (18 inches)

This distinction helps when applying the formula to find the area or solving other geometry problems.

Applying Mathematical Formulas

Applying formulas in mathematics is like following a recipe while cooking. You have set instructions to achieve the desired outcome. Here, our goal is to find the area of the rectangle using the area formula.

First, recall the formula: \[\text{Area} = \text{Length} \times \text{Width}\]Plugging in our values, we have:\[\text{Area} = 24 \text{ inches} \times 18 \text{ inches}\]This step is key because it's where the unknown becomes known. It's where logical thinking meets numbers in a satisfying way. Finally, carry out the multiplication. This gives you 432 square inches.

• Identify the formula needed
• Substitute the correct dimensions
• Solve to find the area

By applying the formula correctly, the abstract numbers transform into a useful measure of space, showing the power of math in everyday situations.