Problem 68 - Elementary Algebra

Question

A computer monitor measures 57.3 centimeters in length and 40.9 centimeters in height. Calculate the total area of the screen.

Step-by-Step Solution

Answer

The area of the screen is 2345.57 cm².

Step 1: Understand the Problem

We are asked to find the area of a computer monitor using length and height measurements. The problem provides the length as 57.3 cm and the height as 40.9 cm.

Step 2: Recall the Formula for Area

To find the area of a rectangle, we use the formula:\[\text{Area} = \text{Length} \times \text{Height}\]

Step 3: Plug in the Values

Insert the given values into the area formula:\[\text{Area} = 57.3 \times 40.9\]

Step 4: Calculate the Area

Perform the multiplication:\[57.3 \times 40.9 = 2345.57\]Therefore, the area of the screen is 2345.57 square centimeters.

Key Concepts

Rectangle Area

Calculating the area of a rectangle is a fundamental concept in geometry. This calculation helps us understand how much space is contained within a rectangle. In simple terms, the area represents the flat, two-dimensional space inside the boundary of the rectangle. This is especially useful for practical applications, like determining the area of a computer monitor screen. To find the area of a rectangle, you'll use two basic measurements: length and height (or alternatively width). These measurements span the two axes of a rectangle: the length runs along the longest side, while the height extends along the shorter side. By understanding these measures, you grasp the physical dimensions that make up the rectangle's total area.
Calculating the area involves multiplying these two measurements together. So, once you have your length and height, you simply multiply them to find the area as per the formula:

• Length: The longer side of the rectangle
• Height: The shorter side of the rectangle
• Area = Length × Height

Measurement Units

In mathematical calculations, understanding measurement units is crucial, as they give context to the magnitude of numbers. In the problem of determining the monitor's area, centimeters are the chosen unit for both length and height, which is common in many parts of the world. Measurement units provide a standardized way to talk about the size of an object. They can vary greatly across different systems, such as metric (centimeters, meters) and imperial (inches, feet) systems.
When calculating area, it is vital to keep the units consistent. For instance, if you start with centimeters, your final result should be in square centimeters. This happens because when you multiply two lengths (length and height), their units also multiply, leading you to square the original unit. Therefore, our answer for the area is 2345.57 square centimeters, where "square centimeters" indicates the two-dimensional measurement of space.

Mathematical Formula

The mathematical formula for finding the area of a rectangle is one of the simplest yet powerful tools in mathematics. The formula is expressed as:\[\text{Area} = \text{Length} \times \text{Height}\]It serves as a guideline to accurately compute the extent of space inside a rectangle. Regardless of the rectangle's size, this formula will help you determine its area effectively.Using this formula is straightforward:

• Make sure you have both the length and height of the rectangle.
• Multiply these two measurements to find the area.
• Always attach the correct unit of measurement squared, such as square centimeters in this case.

Understanding this formula allows you to apply it to various real-world tasks, such as finding the size of screens, books, and rooms. It's widely applicable and a cornerstone of basic geometry.