Trapezoid Perimeter Problem: Finding Missing Side in 30 cm Total Length

Perimeter Calculations with Missing Sides

The perimeter of the trapezoid below is 30 cm. Calculate the length of the missing side.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find side BC
00:03 The perimeter of the trapezoid equals the sum of its sides
00:13 We'll substitute appropriate values according to the given data and solve for BC
00:29 We'll isolate BC
00:38 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

The perimeter of the trapezoid below is 30 cm. Calculate the length of the missing side.

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2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information
  • Step 2: Apply the perimeter formula
  • Step 3: Solve for the missing side

Now, let’s work through each step:

Step 1: The problem gives us a trapezoid with a perimeter of 30 cm and known side lengths of 8 cm, 4 cm, and 12 cm.
We let the missing side be x x cm.

Step 2: Use the perimeter formula for a trapezoid:

30=8+4+12+x 30 = 8 + 4 + 12 + x

Step 3: Combine the known side lengths:

30=24+x 30 = 24 + x

Solve for x x :

x=3024 x = 30 - 24 x=6 x = 6

Therefore, the length of the missing side is 6 cm.

3

Final Answer

6 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter equals sum of all four sides of trapezoid
  • Technique: Add known sides first: 8 + 4 + 12 = 24 cm
  • Check: Verify total: 6 + 8 + 4 + 12 = 30 cm ✓

Common Mistakes

Avoid these frequent errors
  • Adding sides incorrectly or missing one side
    Don't forget to include all four sides in your calculation = incomplete perimeter! Students often add only the labeled sides and forget the unlabeled one. Always identify all four sides of the trapezoid before setting up your equation.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

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What is the area?

FAQ

Everything you need to know about this question

What exactly is the perimeter of a shape?

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The perimeter is the total distance around the outside of a shape. For any polygon, you add up all the side lengths to get the perimeter.

How do I know which side is missing in the diagram?

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Look for the side that doesn't have a number label! In this trapezoid, three sides are labeled (8, 4, and 12), so the fourth unlabeled side is what we need to find.

Can I solve this without setting up an equation?

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Yes! You can think of it as: What number plus 8 + 4 + 12 equals 30? But setting up the equation 30=8+4+12+x 30 = 8 + 4 + 12 + x helps you organize your work clearly.

What if my answer doesn't make sense?

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Always check if your answer is reasonable! If you got a negative number or a very large number, double-check your arithmetic. Side lengths should always be positive.

Do I need to know what type of trapezoid this is?

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No! For perimeter problems, the shape doesn't matter - you just need to add all the sides. Whether it's isosceles, right, or scalene trapezoid, the method stays the same.

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