Calculate the Percentage: Shaded Area in Rectangle Problem

Visual Percentage Estimation with Rectangle Comparison

What percentage does the shaded area of the figure represent?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Estimate the colored part
00:06 Let's divide the drawing in half, it appears more than half is colored
00:12 Let's eliminate the options smaller than half
00:28 Looking at the whole, the colored part isn't as close to 100 as 99
00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What percentage does the shaded area of the figure represent?

2

Step-by-step solution

It can be said with certainty that the shaded area is larger than half of the shape.

That is, the shaded part is more than 50%.

Therefore, we can disregard answers B and D.

The unshaded part is greater than 1% of the figure; it is not possible for 100 such parts to form the complete shape, therefore, we can disregard answer C.

Therefore, the correct answer must be 80%.

3

Final Answer

80%

Key Points to Remember

Essential concepts to master this topic
  • Visual Analysis: Compare shaded area to total rectangle dimensions
  • Elimination Method: Rule out 30% and 10% since shaded > 50%
  • Verification: Check if unshaded portion matches remaining percentage ✓

Common Mistakes

Avoid these frequent errors
  • Trying to calculate exact measurements instead of estimating
    Don't measure pixel by pixel or try to find exact dimensions = unnecessarily complex calculations! Visual percentage problems test estimation skills, not precise measurement. Always use visual comparison and logical elimination to narrow down reasonable answers.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is \( \frac{11}{50} \) written as a percentage?

FAQ

Everything you need to know about this question

How can I tell if the shaded area is more than 50% without measuring?

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Look at the visual balance! If the shaded area clearly takes up more space than the unshaded area, it's definitely over 50%. In this rectangle, the shaded portion is obviously larger than the small unshaded strip.

Why can't the answer be 99% if most of the rectangle is shaded?

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The unshaded area is much larger than 1% of the total rectangle! If the answer were 99%, the unshaded part would be tiny - but you can see it's a substantial strip on the left side.

Is there a formula for calculating percentage of shaded areas?

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Yes! The formula is Shaded AreaTotal Area×100% \frac{\text{Shaded Area}}{\text{Total Area}} \times 100\% . But for visual estimation problems like this, you use logical reasoning and elimination instead.

What if I can't decide between two remaining answers?

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Compare the sizes more carefully! Ask yourself: "Is the unshaded part about 1/5 of the total (suggesting 80%) or much smaller?" The visual evidence will guide you to the right choice.

Do I need to know exact measurements to solve percentage problems?

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Not for visual estimation! These problems test your ability to reasonably estimate proportions. Use your eyes to compare areas and logical thinking to eliminate impossible answers.

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