Calculate the Area: Finding Units in an Orange-Shaded Grid Rectangle

Area Calculation with Grid Fraction Analysis

Determine the numerical value of the shaded area:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the numerical value of the shaded area:

2

Step-by-step solution

To solve this problem, let's follow the outlined plan:

  • Step 1: Count the number of shaded sections.
  • Step 2: Count the total number of sections in the rectangle.
  • Step 3: Express the number of shaded sections as a fraction of the total sections.
  • Step 4: Convert this fraction to a decimal to find the numerical value.

Now, let's apply these steps:
Step 1: The given diagram shows that there are 4 vertical stripes shaded.
Step 2: The total number of vertical stripes (including both shaded and unshaded) is 10.
Step 3: The fraction of shaded area is 410\frac{4}{10}.
Step 4: Convert 410\frac{4}{10} to a decimal. This equals 0.40.4.

Therefore, the numerical value of the shaded area is 0.4.

3

Final Answer

0.4

Key Points to Remember

Essential concepts to master this topic
  • Grid Method: Count shaded sections compared to total sections
  • Technique: Express as fraction: 4 shaded out of 10 total = 410\frac{4}{10}
  • Check: Convert fraction to decimal: 410=0.4\frac{4}{10} = 0.4 matches answer ✓

Common Mistakes

Avoid these frequent errors
  • Miscounting the total number of sections
    Don't count only the shaded sections or visible grid lines = wrong denominator! This gives you 44=1.0\frac{4}{4} = 1.0 instead of the correct 0.4. Always count all sections in the entire rectangle, both shaded and unshaded.

Practice Quiz

Test your knowledge with interactive questions

Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

How do I know which sections to count as the total?

+

Look at the entire rectangle and count all vertical strips from left to right. In this problem, there are 10 total strips, even though only 4 are shaded orange.

Why do we convert the fraction to a decimal?

+

The question asks for the numerical value, which typically means decimal form. Converting 410\frac{4}{10} to 0.4 gives the clearest answer format.

What if the shaded area doesn't line up perfectly with grid lines?

+

In this type of problem, the shaded region will always align with the grid boundaries. Count complete sections only - no partial sections to worry about!

Can I simplify the fraction before converting to decimal?

+

Yes! 410=25\frac{4}{10} = \frac{2}{5} both equal 0.4. Simplifying first can make the decimal conversion easier, but either method works.

How can I double-check my counting?

+

Use the grid pattern! Count by looking at the vertical lines - they separate the sections. With 11 vertical lines, you get 10 sections between them.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations