Calculate the Perimeter of an Isosceles Trapezoid with Sides 10, 12, and 6

Isosceles Trapezoid Perimeter with Side Calculations

Below is an isosceles trapezoid:

101010121212666 What is its perimeter?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 Let's calculate the perimeter of the trapezoid together.
00:15 We'll use the side lengths provided in the problem.
00:19 Remember, in an isosceles trapezoid, two sides are equal.
00:28 The perimeter is the total length of all the sides added together.
00:41 Let's plug in the values and find the perimeter step by step.
00:52 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is an isosceles trapezoid:

101010121212666 What is its perimeter?

2

Step-by-step solution

To calculate the perimeter of the isosceles trapezoid, we follow these steps:

  • Identify the lengths of all the sides.
  • Sum these lengths to find the perimeter.

Now, let's apply these steps:
Step 1: The given lengths of the trapezoid are:
- Base 1 = 1010,
- Base 2 = 1212,
- Each leg = 66.

Step 2: Using the perimeter formula P=a+b+c+d P = a + b + c + d , we get:
P=10+12+6+6 P = 10 + 12 + 6 + 6 .

Step 3: Adding these values, we find:
P=34 P = 34 .

Therefore, the perimeter of the isosceles trapezoid is 34 34 .

3

Final Answer

34

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add all four sides to find the perimeter
  • Technique: Identify equal legs: 6 + 6 + 10 + 12 = 34
  • Check: Count all sides twice: two bases plus two legs = 4 total ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the second leg side
    Don't add just 10 + 12 + 6 = 28! This ignores the second leg side in an isosceles trapezoid. Always remember that isosceles trapezoids have two equal legs, so add both: 10 + 12 + 6 + 6 = 34.

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

What makes this trapezoid 'isosceles'?

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An isosceles trapezoid has two equal legs (the slanted sides). In this problem, both legs measure 6 units, making it isosceles.

How do I know which sides are the legs and which are the bases?

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The bases are the parallel sides (top and bottom), while the legs are the slanted sides that connect them. Here: bases are 10 and 12, legs are both 6.

Why do I need to add the same leg measurement twice?

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Because there are two separate legs! Even though they're equal in length (6 each), you still have to count both of them when finding the perimeter.

Can I use a formula for isosceles trapezoid perimeter?

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Yes! The formula is P=b1+b2+2l P = b_1 + b_2 + 2l where b1 b_1 and b2 b_2 are the bases and l l is one leg length.

What if the diagram doesn't clearly show all measurements?

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Look for labels on each side of the trapezoid. In isosceles trapezoids, if one leg is labeled, the other leg has the same length even if not explicitly shown.

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