Problem 60 - Prealgebra

Question

This stamp was issued in 2001 to honor the Italian scientist Enrico Fermi. The image area of the stamp has a width of 21.4 millimeters and a length of 35.8 millimeters. Find the area of the image. Round to the nearest whole number.

Step-by-Step Solution

Answer

The area of the image is 765 square millimeters.

Step 1: Understanding the problem

We need to find the area of a rectangle, which is the image area of a stamp, for which the width and length are given in millimeters. The formula for the area of a rectangle is width multiplied by length. Once calculated, we will round the result to the nearest whole number.

Step 2: Applying the formula for area

The formula for the area of a rectangle is given by the equation \( A = ext{width} imes ext{length} \). Here, we substitute the given values: width = 21.4 mm and length = 35.8 mm.

Step 3: Calculating the area

Substitute the given values into the formula: \[ A = 21.4 imes 35.8 \] Multiply the values to find the area: \[ A = 765.32 ext{ mm}^2 \]

Step 4: Rounding the result

The calculated area is 765.32 square millimeters. We round this number to the nearest whole number. Since the decimal part (.32) is less than 0.5, we round down to 765.

Key Concepts

Unit Conversion

Understanding unit conversion is key in many math and science problems. Here, the area of a rectangle is found in square millimeters. However, let’s dive deeper into unit conversion concepts.

• Why Convert Units?
  Sometimes calculations require converting unit measurements to ensure consistency. For example, converting millimeters to centimeters or inches can be necessary for other problems.
  
• Conversions Explained
  To convert measurements, use conversion factors:
  • 1 centimeter = 10 millimeters.
  • 1 meter = 1000 millimeters.
  • 1 inch = 25.4 millimeters.
  To convert, multiply or divide by the conversion factor. So, for 21.4 mm to cm: divide 21.4 by 10, resulting in 2.14 cm.
  

It's essential to be proficient in these conversions to solve problems effectively.

Rounding Numbers

Rounding numbers makes them easier to work with or understand, especially when not all decimal digits are needed. Here, after calculating the area as 765.32 square millimeters, rounding to the nearest whole number was required.

• How to Round Numbers
  The basic rule for rounding is:
  • If the decimal is 5 or more, round up.
  • If it's less than 5, round down.
  In our example, 765.32 becomes 765, since 0.32 is less than 0.5.
  
• Why Round Numbers?
  Rounding helps simplify figures, making them more practical for everyday use, like in measurement and finances.
  

Remember, while rounding, precision depends on the context, as requirements might vary.

Geometry Basics

A strong grasp of geometry basics is fundamental for many problems, like finding the area of a rectangle.

• The Formula for Rectangle's Area
  To find the area: multiply width by length. For our stamp, it’s
  \[ A = 21.4 \times 35.8 = 765.32 \text{ mm}^2 \]
  
• Key Geometry Terms
  Understanding geometry requires knowing a few terms:
  • Length: The longer side of the rectangle.
  • Width: The shorter side of the rectangle.
  • Area: The amount of space inside the rectangle, in square units.
  These concepts are foundational and necessary for solving similar problems.
  

Reviewing basic geometry ensures solving related problems becomes an easier task.