Trapezoid Perimeter: Finding the Total Length with a 1.5 Base Ratio

Trapezoid Perimeter with Base Ratio

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

222333555

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the perimeter of the trapezoid
00:05 The perimeter of the trapezoid equals the sum of its sides
00:28 Substitute the side value according to the given ratio
00:43 Substitute appropriate values and solve to find the perimeter
01:09 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

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

222333555

2

Step-by-step solution

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

5×1.5=7.5 5\times1.5=7.5

Now we will add up all the sides to find the perimeter:

2+5+3+7.5=7+3+7.5=10+7.5=17.5 2+5+3+7.5=7+3+7.5=10+7.5=17.5

3

Final Answer

17.5

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter equals sum of all four sides
  • Technique: Calculate long base: 5×1.5=7.5 5 \times 1.5 = 7.5
  • Check: Add all sides: 2 + 5 + 3 + 7.5 = 17.5 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to calculate the long base length
    Don't add up the given measurements without finding the long base first = incomplete perimeter! You only see three measurements (2, 3, 5) but need all four sides. Always multiply the short base by the given ratio to find the missing long base length.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

FAQ

Everything you need to know about this question

How do I know which base is the short one and which is the long one?

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Look at the diagram carefully! The short base is labeled as 5 units, and we're told the long base is 1.5 times longer. So the long base = 5×1.5=7.5 5 \times 1.5 = 7.5 units.

Why can't I just add 2 + 3 + 5 = 10 for the perimeter?

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Because a trapezoid has four sides, not three! You're missing the long base. The perimeter needs all four sides: both legs (2 and 3), the short base (5), and the long base (7.5).

What does '1.5 times longer' actually mean?

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It means the long base is 1.5 times the length of the short base. So if the short base is 5 units, then: 5×1.5=7.5 5 \times 1.5 = 7.5 units for the long base.

How do I remember the perimeter formula for trapezoids?

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Simple! Perimeter = sum of all sides for any polygon. For a trapezoid: P = leg₁ + leg₂ + short base + long base. Just add up everything around the outside!

Can the ratio be a decimal like 1.5?

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Absolutely! Ratios can be decimals, fractions, or whole numbers. 1.5 means the long base is one and a half times the short base length.

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