Trapezoid Perimeter Problem: Finding Missing Side CD When Total is 22 cm

Q: How do I know which measurements are the actual sides?

Look at the diagram carefully! The sides are the edges that form the trapezoid's boundary. In this problem, AB is clearly a side (length 7), and AC and BD appear to be the slanted sides (both length 3).

Q: What if the diagram is confusing about which sides are which?

Focus on the labels given in the problem. If you're told specific measurements like AB = 7 cm, that means AB is definitely one of the four sides forming the perimeter.

Q: Why do I subtract instead of just adding everything?

Because we're solving for the unknown! We know the total perimeter (22) and three side lengths, so: $ CD = 22 - 7 - 3 - 3 = 9 $

Q: How do I check my answer is reasonable?

Ask yourself: Does this make sense? CD = 9 cm is reasonable because it's similar to the other given side lengths (7, 3, 3), and 9 + 7 + 3 + 3 = 22 matches the given perimeter.

Perimeter Calculations with Unknown Side Lengths

The perimeter of the trapezoid equals 22 cm.

AB = 7 cm

AC = 3 cm

BD = 3 cm

What is the length of side CD?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find CD

00:03 The perimeter of a trapezoid equals the sum of its sides

00:10 We'll substitute appropriate values and solve for CD

00:31 Let's group terms

00:36 Let's isolate CD

00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The perimeter of the trapezoid equals 22 cm.

AB = 7 cm

AC = 3 cm

BD = 3 cm

What is the length of side CD?

Step-by-step solution

Since we are given the perimeter of the trapezoid and not the length of CD, we can calculate:

$22=3+3+7+CD$

$22=CD+13$

$22-13=CD$

$9=CD$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: Add all four sides of the trapezoid together
Technique: Set up equation: 22 = 7 + 3 + 3 + CD
Check: Verify CD = 9: 7 + 3 + 3 + 9 = 22 ✓

Common Mistakes

Avoid these frequent errors

Confusing which measurements represent side lengths
Don't assume AC and BD are sides of the trapezoid = wrong setup! These could be diagonals or heights. Always identify the actual sides (AB, BC, CD, DA) from the diagram before writing your perimeter equation.

Practice Quiz

Test your knowledge with interactive questions

True OR False:

In all isosceles trapezoids the base Angles are equal.

FAQ

Everything you need to know about this question

How do I know which measurements are the actual sides?

Look at the diagram carefully! The sides are the edges that form the trapezoid's boundary. In this problem, AB is clearly a side (length 7), and AC and BD appear to be the slanted sides (both length 3).

What if the diagram is confusing about which sides are which?

Focus on the labels given in the problem. If you're told specific measurements like AB = 7 cm, that means AB is definitely one of the four sides forming the perimeter.

Why do I subtract instead of just adding everything?

Because we're solving for the unknown! We know the total perimeter (22) and three side lengths, so: $CD = 22 - 7 - 3 - 3 = 9$

Can a trapezoid have sides of different lengths?

Absolutely! Unlike rectangles or squares, trapezoids can have all four sides different lengths. Only the parallel sides need to follow specific rules.

How do I check my answer is reasonable?

Ask yourself: Does this make sense? CD = 9 cm is reasonable because it's similar to the other given side lengths (7, 3, 3), and 9 + 7 + 3 + 3 = 22 matches the given perimeter.

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