Find the Missing Side AD in a Trapezoid with 42cm Perimeter

Q: What if I can't remember which sides are which in the diagram?

Look at the labels on each side in the diagram. The sides are AB = 14, BC = 7, CD = 12, and we need to find AD. It doesn't matter which order you add them!

Q: Why do we subtract instead of divide or use another operation?

Because perimeter is addition! When we know the total (42) and three parts (14 + 7 + 12), we subtract to find the missing part. It's like: 5 + ? = 12, so ? = 12 - 5.

Q: How can I check if my answer makes sense?

Ask yourself: Does 9 cm seem reasonable? It's similar to the other sides (7, 12, 14), so it makes sense. Also, add all four sides to verify you get 42 cm.

Q: What if the trapezoid looks different than this one?

The same method works for any quadrilateral! Just add the three known sides and subtract from the given perimeter. The shape's appearance doesn't change the calculation.

Q: Can the missing side be longer than the perimeter?

Never! Each side must be shorter than the total perimeter. If you get an answer larger than 42 cm, double-check your arithmetic - you made an error somewhere.

Trapezoid Perimeter with Missing Side

What is the length of side AD given that the perimeter of the trapezoid is equal to 42 cm?

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Understand the problem

What is the length of side AD given that the perimeter of the trapezoid is equal to 42 cm?

Step-by-step solution

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

Step 1: Identify the given perimeter and side lengths.
Step 2: Use the perimeter formula for a trapezoid.
Step 3: Solve for the missing side $AD$ .

Let's begin:

Step 1: We know that the perimeter $P = 42$ cm. The other sides are $AB = 14$ cm, $BC = 7$ cm, and $CD = 12$ cm.

Step 2: The formula for the perimeter is:

$P = AB + BC + CD + AD$

Substituting in the known values:

$42 = 14 + 7 + 12 + AD$

Step 3: Simplify the equation to find $AD$ :

$42 = 33 + AD$

Subtract 33 from both sides:

$AD = 42 - 33$

$AD = 9$

Therefore, the length of side $AD$ is $\textbf{9 cm}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Sum all four sides of the trapezoid to get total
Technique: Add known sides: 14 + 7 + 12 = 33, then subtract from perimeter
Check: Verify 9 + 14 + 7 + 12 = 42 cm matches given perimeter ✓

Common Mistakes

Avoid these frequent errors

Adding sides incorrectly or forgetting one side
Don't skip any side when adding 14 + 7 + 12 = 32 instead of 33! This leads to AD = 10 instead of 9. Always double-check that you've included all given side lengths before subtracting from the perimeter.

Practice Quiz

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

FAQ

Everything you need to know about this question

What if I can't remember which sides are which in the diagram?

Look at the labels on each side in the diagram. The sides are AB = 14, BC = 7, CD = 12, and we need to find AD. It doesn't matter which order you add them!

Why do we subtract instead of divide or use another operation?

Because perimeter is addition! When we know the total (42) and three parts (14 + 7 + 12), we subtract to find the missing part. It's like: 5 + ? = 12, so ? = 12 - 5.

How can I check if my answer makes sense?

Ask yourself: Does 9 cm seem reasonable? It's similar to the other sides (7, 12, 14), so it makes sense. Also, add all four sides to verify you get 42 cm.

What if the trapezoid looks different than this one?

The same method works for any quadrilateral! Just add the three known sides and subtract from the given perimeter. The shape's appearance doesn't change the calculation.

Can the missing side be longer than the perimeter?

Never! Each side must be shorter than the total perimeter. If you get an answer larger than 42 cm, double-check your arithmetic - you made an error somewhere.

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