Calculate Trapezoid Perimeter: Finding the Sum of 10, 12, and Two 7-Unit Sides

Trapezoid Perimeter with Equal Side Lengths

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

777101010777121212AAABBBCCCDDD

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1

Understand the problem

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

777101010777121212AAABBBCCCDDD

2

Step-by-step solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

  • List the lengths of the sides: the bases are 1010 and 1212, and the two non-parallel sides are each 77.
  • Apply the perimeter formula for a trapezoid: P=a+b+c+d P = a + b + c + d .
  • Substitute the given values into the formula: P=10+12+7+7 P = 10 + 12 + 7 + 7 .
  • Calculate the sum: P=10+12+7+7=36 P = 10 + 12 + 7 + 7 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

This matches the correct answer choice from the provided options.

3

Final Answer

36

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Rule: Add all four sides of the trapezoid together
  • Technique: Identify sides: P=10+12+7+7=36 P = 10 + 12 + 7 + 7 = 36
  • Check: Count all four sides and verify no side was missed or counted twice ✓

Common Mistakes

Avoid these frequent errors
  • Only adding the two bases
    Don't just add the parallel sides 10 + 12 = 22! This gives only part of the perimeter and ignores the two slanted sides. Always add all four sides: both bases plus both non-parallel sides.

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's the difference between area and perimeter for a trapezoid?

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Perimeter is the distance around the outside (add all sides). Area is the space inside (use the area formula). For this problem, we only need perimeter!

Do I need to know which sides are parallel to find perimeter?

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No! For perimeter, it doesn't matter which sides are parallel. Just add up all four side lengths regardless of their position or orientation.

What if the trapezoid has different side lengths?

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The method stays the same! Add all four sides together, no matter what their individual lengths are. Perimeter = side₁ + side₂ + side₃ + side₄.

How do I identify all the sides from the diagram?

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Look for the labeled measurements on each edge of the shape. Count carefully: this trapezoid has sides of 10, 12, 7, and 7 units.

Why are two sides the same length in this trapezoid?

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This is called an isosceles trapezoid - the two non-parallel sides have equal length. This makes the calculation easier since you can write it as 10+12+7+7 10 + 12 + 7 + 7 or 10+12+2(7) 10 + 12 + 2(7) .

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