Calculate Trapezoid Perimeter: Finding the Sum of Sides 9, 12, 5, and 4

Q: What's the difference between perimeter and area?

Perimeter is the distance around the outside edge (add all sides), while area is the space inside the shape (multiply length × width for rectangles). For this trapezoid, we only add the sides!

Q: Do I need to know it's a trapezoid to find perimeter?

No! The perimeter formula works for any polygon - triangle, square, pentagon, etc. Just add up all the side lengths, no matter what shape it is.

Q: What if the sides are in different units?

Always convert to the same unit first! If one side is in meters and another in centimeters, change them all to the same unit before adding.

Q: How can I double-check my addition?

Try adding in a different order: (9 + 12) + (5 + 4) = 21 + 9 = 30. You can also use a calculator or add backwards: 30 - 4 - 12 - 5 - 9 = 0 ✓

Q: Why does the shape matter if I just add the sides?

Great observation! For perimeter, the shape doesn't matter - you always add sides. The trapezoid shape would matter if we were calculating area, which uses different formulas for different shapes.

Perimeter Calculation with Four-Sided Polygons

Calculate the perimeter of the trapezoid below:

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the perimeter of the trapezoid below:

Step-by-step solution

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

Step 1: Identify the given side lengths of the trapezoid.
Step 2: Use the perimeter formula for a trapezoid, which is the sum of the lengths of its sides.
Step 3: Perform the necessary addition to compute the perimeter.

Now, let's work through each step:
Step 1: The trapezoid has side lengths of $9$ , $5$ , $12$ , and $4$ .
Step 2: The formula for the perimeter $P$ of a trapezoid is:
$P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4$
Step 3: Plugging in the values, we compute:
$P = 9 + 5 + 12 + 4$
Step 4: Calculating the sum:
$P = 30$

Therefore, the perimeter of the trapezoid is $30$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals the sum of all side lengths
Technique: Add all sides: 9 + 5 + 12 + 4 = 30
Check: Count four sides and verify addition: 9+5=14, 14+12=26, 26+4=30 ✓

Common Mistakes

Avoid these frequent errors

Multiplying sides instead of adding them
Don't multiply the sides like 9 × 5 × 12 × 4 = 2,160! This calculates area or volume, not perimeter. Perimeter is distance around the outside, so always add all the side lengths together.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

What's the difference between perimeter and area?

Perimeter is the distance around the outside edge (add all sides), while area is the space inside the shape (multiply length × width for rectangles). For this trapezoid, we only add the sides!

Do I need to know it's a trapezoid to find perimeter?

No! The perimeter formula works for any polygon - triangle, square, pentagon, etc. Just add up all the side lengths, no matter what shape it is.

What if the sides are in different units?

Always convert to the same unit first! If one side is in meters and another in centimeters, change them all to the same unit before adding.

How can I double-check my addition?

Try adding in a different order: (9 + 12) + (5 + 4) = 21 + 9 = 30. You can also use a calculator or add backwards: 30 - 4 - 12 - 5 - 9 = 0 ✓

Why does the shape matter if I just add the sides?

Great observation! For perimeter, the shape doesn't matter - you always add sides. The trapezoid shape would matter if we were calculating area, which uses different formulas for different shapes.

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