Calculate the Perimeter of an Isosceles Trapezoid with Sides 3, 5, and 7

Perimeter Calculation with Given Side Lengths

The drawing shows an isosceles trapezoid.

What is its perimeter?

333555777

❤️ Continue Your Math Journey!

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

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
00:25 Equal sides in an isosceles trapezoid
00:35 Let's substitute appropriate values and solve for the perimeter
00:58 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The drawing shows an isosceles trapezoid.

What is its perimeter?

333555777

2

Step-by-step solution

To find the perimeter of the isosceles trapezoid, consider the following steps:

  • Step 1: Identify the given side lengths: The top base of the trapezoid is 33, each of the slanted sides is 55, and the bottom base is 77.
  • Step 2: Apply the perimeter formula: The perimeter PP is the sum of all side lengths: P=3+5+5+7P = 3 + 5 + 5 + 7.
  • Step 3: Perform the calculation: Add the side lengths together:
    3+5+5+7=20 3 + 5 + 5 + 7 = 20

Therefore, the perimeter of the isosceles trapezoid is 2020.

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perimeter equals the sum of all side lengths
  • Technique: Add all four sides: 3+5+5+7=20 3 + 5 + 5 + 7 = 20
  • Check: Count each side once: top + right + bottom + left = 4 sides total ✓

Common Mistakes

Avoid these frequent errors
  • Missing one of the equal sides in calculation
    Don't add just 3 + 5 + 7 = 15! This ignores that an isosceles trapezoid has two equal slanted sides. Always remember that 'isosceles' means two sides are equal, so count both 5-unit sides.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the trapezoid according to the following data:

777101010777121212AAABBBCCCDDD

FAQ

Everything you need to know about this question

What does 'isosceles trapezoid' mean?

+

An isosceles trapezoid has two parallel bases (top and bottom) and two equal slanted sides. In this problem, both slanted sides are 5 units long.

How do I know which sides are equal?

+

Look at the diagram carefully! The two slanted sides (legs) are both labeled with the same number. Here, both diagonal sides show 5, so they're equal.

Do I need to use any special trapezoid formulas?

+

No! For perimeter, you simply add up all the side lengths. Special formulas are only needed for area calculations.

What if the diagram doesn't show all side lengths?

+

In an isosceles trapezoid, if you know three sides, you can find the fourth! The two legs are always equal, so if one leg is given, the other leg has the same length.

Can I solve this without the diagram?

+

Yes! As long as you know it's an isosceles trapezoid with sides 3, 5, and 7, you know the pattern: one base is 3, both legs are 5, and the other base is 7.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Trapeze 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