Calculate the Trapezoid's Perimeter: Using Given Base and Side Lengths

Q: Do I need to identify which sides are parallel?

For finding perimeter, it doesn't matter which sides are parallel! You simply add all four side lengths together, regardless of the trapezoid's orientation or which sides are bases.

Q: Can I add the numbers in any order?

Yes! Addition is commutative, so you can add the four side lengths in whatever order is easiest for you. The result will always be the same.

Trapezoid Perimeter with Four Given Sides

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 use the perimeter formula for a trapezoid, which is straightforward since all side lengths are provided:

Step 1: Identify the side lengths:
Top base ( $a$ ): $12.28$ units
Bottom base ( $b$ ): $17.5$ units
Left non-parallel side ( $c$ ): $5.1$ units
Right non-parallel side ( $d$ ): $6$ units
Step 2: Apply the formula for the perimeter, which states:
$P = a + b + c + d$
Step 3: Substitute the known values into the formula:
$P = 12.28 + 17.5 + 5.1 + 6$
Step 4: Perform the addition:

Calculating the sum:

$12.28 + 17.5 = 29.78$

$29.78 + 5.1 = 34.88$

$34.88 + 6 = 40.88$

Hence, the perimeter of the trapezoid is $40.88$ units.

Final Answer

40.88

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four side lengths
Technique: Add systematically: 12.28 + 17.5 + 5.1 + 6 = 40.88
Check: Count all sides in diagram and verify addition is correct ✓

Common Mistakes

Avoid these frequent errors

Counting only two parallel bases
Don't add just 12.28 + 17.5 = 29.78 and call it done! This ignores the non-parallel sides and gives an incomplete perimeter. Always include all four sides: both bases plus both legs.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

Do I need to identify which sides are parallel?

For finding perimeter, it doesn't matter which sides are parallel! You simply add all four side lengths together, regardless of the trapezoid's orientation or which sides are bases.

What if the trapezoid looks tilted or rotated?

The shape's orientation doesn't change the perimeter calculation. Whether the trapezoid is upright, tilted, or flipped, you still add all four given side lengths.

How do I make sure I'm reading all the measurements correctly?

Look carefully at each side of the trapezoid and match it to its labeled measurement. In this problem: 12.28, 17.5, 5.1, and 6 are the four sides you need.

Should I worry about units in my final answer?

Always include the same units as given in the problem. Since all measurements here are in units, your perimeter should also be expressed as 40.88 units.

Can I add the numbers in any order?

Yes! Addition is commutative, so you can add the four side lengths in whatever order is easiest for you. The result will always be the same.

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